6. Exponential & Logarithmic Functions

Solving Exponential and Logarithmic Equations

Open Question
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 x+log 4
Multiple Choice
Solve the exponential equation.
$4^{x+7}=16$
Multiple Choice
Solve the exponential equation.
$100^{x}=10^{x+17}$
Multiple Choice
Solve the exponential equation.
$81^{x+1}=27^{x+5}$
Multiple Choice
Solve the exponential equation.
$2\cdot10^{3x}=5000$
Multiple Choice
Solve the exponential equation.
$900=10^{x+17}$
Multiple Choice
Solve the exponential equation.
$e^{2x+5}=8$
Multiple Choice
Solve the exponential equation.
$7^{2x^2-8}=1$
Multiple Choice
Solve the logarithmic equation.
$\log_3\left(3x+9\right)=\log_35+\log_312$
Multiple Choice
Solve the logarithmic equation.
$\log\left(x+2\right)+\log2=3$
Multiple Choice
Solve the logarithmic equation.
$\log_7\left(6x+13\right)=2$
Open Question
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64
Open Question
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
Open Question
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
Open Question
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