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. log(x+4)=log x+log 4

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\(\cdot\)10^{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\(\right\))+\(\log\)2=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