6. Exponential & Logarithmic Functions

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. ln(x−4)+ln(x+1)=ln(x−8)

Solve the exponential equation.

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

Solve each equation. Give solutions in exact form. 5 ln x = 10

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

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. 6^(x+1) = 4^(2x-1)

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 32^x=8

Solve each equation. Give solutions in exact form. See Examples 5–9. log x + log(x - 21) = log 100

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = 5^x, g(x) = log￬5 x

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. $\ln \sqrt{x+3}=1$

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. (1/3)^x = -3

Solve the exponential equation.

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

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. 6+2 ln x=5

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. 0.05(1.15)^x = 5

In Exercises 74–79, solve each logarithmic equation. log2 (x+3) + log2 (x-3) =4

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. e^4x+5e^2x−24=0