# Solving Exponential and Logarithmic Equations - Video Tutorials & Practice Problems

## Solving Exponential Equations Using Like Bases

Solve the exponential equation.

$4^{x+7}=16$

2

5

9

– 5

Solve the exponential equation.

$100^{x}=10^{x+17}$

17

34

8.5

0

Solve the exponential equation.

$81^{x+1}=27^{x+5}$

– 13

11

14

3

## Solving Exponential Equations Using Logs

Solve the exponential equation.

$2\cdot10^{3x}=5000$

$x=3.40$

$x=10.19$

$x=0.0001$

$x=1.13$

Solve the exponential equation.

$900=10^{x+17}$

$x=-14.05$

$x=2.95$

$x=0.17$

$x=1.72$

Solve the exponential equation.

$e^{2x+5}=8$

$x=-1.46$

$x=-1.11$

$x=-0.22$

$x=1.39$

Solve the exponential equation.

$7^{2x^2-8}=1$

$x=0.51$

$x=\pm2$

$x=\pm2.83$

$x=2.23$

## Solving Logarithmic Equations

Solve the logarithmic equation.

$\log_3\left(3x+9\right)=\log_35+\log_312$

20

17

1

No Solution

Solve the logarithmic equation.

$\log\left(x+2\right)+\log2=3$

498

1998

6

No Solution

Solve the logarithmic equation.

$\log_7\left(6x+13\right)=2$

3

19.17

6

No Solution

## Do you want more practice?

- Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then...
- Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then...
- Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then...
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousand...
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousand...
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousand...
- Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or...
- Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or...
- Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or...
- Graph f(x) = 2^x and g(x) = log2 x in the same rectangular coordinate system. Use the graphs to determine each...
- Solve each equation. Give solutions in exact form. See Examples 5–9. 5 ln x = 10
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln 4x = 1.5
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(2 - x) = 0.5
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(2 - x) = 0.5
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_6 (2x + 4) = 2
- Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain...
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_4 (x^3 + 37) = 3
- Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain...
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln x + ln x^2 = 3
- Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain...
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_3 [(x + 5)(x - 3)] = 2
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 [(2x + 8)(x + 4)] = 5
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_5 [(3x + 5)(x + 1)] = 1
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(x + 25) = log(x + 10) + log 4
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(3x + 5) - log(2x + 4) = 0
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(3x + 5) - log(2x + 4) = 0
- In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support you...
- In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support you...
- In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support you...
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln(7 - x) + ln(1 - x) = ln (25 - x)
- In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of nat...
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_8 (x + 2) + log_8 (x + 4) = log_8 8
- In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of nat...
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 (x^2 - 100) - log_2 (x + 10) = 1
- In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of nat...
- Solve each equation. Give solutions in exact form. See Examples 5–9. log x + log(x - 21) = log 100
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(9x + 5) = 3 + log(x + 2)
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(9x + 5) = 3 + log(x + 2)
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln(4x - 2) - ln 4 = -ln(x - 2)
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln(5 + 4x) - ln(3 + x) = ln 3
- Solve each equation. Give solutions in exact form. See Examples 5–9. . log_5 (x + 2) + log_5 (x - 2) = 1
- Solve each equation. Give solutions in exact form. See Examples 5–9. . log_5 (x + 2) + log_5 (x - 2) = 1
- In Exercises 74–79, solve each logarithmic equation. log2 (x+3) + log2 (x-3) =4
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 (2x - 3) + log_2 (x + 1) = 1
- In Exercises 74–79, solve each logarithmic equation. log4 (2x+1) = log4 (x-3) + log4 (x+5)
- In Exercises 74–79, solve each logarithmic equation. log4 (2x+1) = log4 (x-3) + log4 (x+5)
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln e^x - 2 ln e = ln e^4
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 (log_2 x) = 1
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 (log_2 x) = 1
- Solve each equation. Give solutions in exact form. See Examples 5–9. log x^2 = (log x)^2
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. p =...
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. r =...
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. I =...
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y =...
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y =...
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y =...
- In Exercises 93–102, solve each equation. 5^2x ⋅ 5^4x=125
- In Exercises 93–102, solve each equation. 3^x+2 ⋅ 3^x=81
- In Exercises 93–102, solve each equation. 3^x+2 ⋅ 3^x=81
- In Exercises 93–102, solve each equation. 2|ln x|−6=0
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. log...
- In Exercises 93–102, solve each equation. 3|log x|−6=0
- In Exercises 93–102, solve each equation. 3^x2=45
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. A =...
- In Exercises 93–102, solve each equation. ln(2x+1)+ln(x−3)−2 ln x=0
- In Exercises 93–102, solve each equation. ln 3−ln(x+5)−ln x=0
- In Exercises 93–102, solve each equation. ln 3−ln(x+5)−ln x=0
- In Exercises 93–102, solve each equation. 5^(x^2−12)=25^2x
- To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^(tn) and A = Pe^(rt) Find...
- To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^(tn) and A = Pe^(rt) At w...
- To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^(tn) and A = Pe^(rt) At w...
- Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = 5^x, g(x) = log￬5 x
- Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬2 x+1, g(x) = 2^x-1
- Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬4 (x+3), g(x) = 4^x + 3
- Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 3^x
- Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 3^x
- Write an equation for the inverse function of each one-to-one function given. ƒ(x) = (1/3)^x
- Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^(x-5)
- Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 5^x + 1
- Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 4^x+2
- Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^x + 10
- Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^(x+1) - 4
- Find ƒ^-1(x), and give the domain and range. ƒ(x) = 2 ln 3x
- Find the error in the following 'proof' that 2 < 1.
- Find the error in the following 'proof' that 2 < 1.
- Exercises 137–139 will help you prepare for the material covered in the next section. Solve for x: a(x - 2) =...
- Exercises 137–139 will help you prepare for the material covered in the next section. Solve: x(x - 7) = 3.
- Exercises 137–139 will help you prepare for the material covered in the next section. Solve: (x + 2)/(4x + 3)...