6. Exponential & Logarithmic Functions

Solve each equation. Give solutions in exact form. See Examples 5–9. log(3x + 5) - log(2x + 4) = 0

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 equation. Give solutions in exact form. log₂ [(2x + 8)(x + 4)] = 5

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log₂(x+2)−log₂(x−5)=3

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (log2 x)^4 = 4 log2 x

Solve each equation. Give solutions in exact form. See Examples 5–9. log₂ (x² - 100) - log₂ (x + 10) = 1

Solve the logarithmic equation.

$\(\log\)_7\(\left\)(6x+13\(\right\))=2$

Solve each equation. Give solutions in exact form. log₆ (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 of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2 log x=log 25

Solve each equation. Give solutions in exact form. See Examples 5–9. . log₅ (x + 2) + log₅ (x - 2) = 1

Solve each equation. Give solutions in exact form. log₄ (x³ + 37) = 3

To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^tn and A = Pe^rt Find t, to the nearest hundredth of a year, if \$1786 becomes \$2063 at 2.6%, with interest compounded monthly.

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. ln(7 - x) + ln(1 - x) = ln (25 - x)