6. Exponential & Logarithmic Functions

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2^(4x-2) = 64

Solve each equation. Give solutions in exact form. See Examples 5–9. log(9x + 5) = 3 + log(x + 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. log(x+4)−log 2=log(5x+1)

Solve the exponential equation.

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

Solve each equation. Give solutions in exact form. log₂ (log₂ x) = 1

Solve each equation. Give solutions in exact form. See Examples 5–9. log₂ (2x - 3) + log₂ (x + 1) = 1

Solve each equation. ln 3−ln(x+5)−ln x=0

Solve the exponential equation.

$900=10^{x+17}$

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. r = p - k ln t, for t

Solve the exponential equation.

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

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 5^x + 1

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. 7^(x+2)=410

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. e^3x-7 • e^-2x = 4e

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. log₃(x+4)=−3