6. Exponential & Logarithmic Functions

Solve the exponential equation.

$4^{x+7}=16$

Solve the exponential equation.

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

Solve the exponential equation.

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

Solve the exponential equation.

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

Solve the exponential equation.

$900=10^{x+17}$

Solve the exponential equation.

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

Solve the exponential equation.

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

Solve the logarithmic equation.

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

Solve the logarithmic equation.

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

Solve the logarithmic equation.

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

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5^x=125

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^2x-1=32

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 4^2x−1=64

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 9^x=27

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 3^x = 7