Solve the exponential equation.
$100^{x}=10^{x+17}$

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

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

Solve the exponential equation.

$4^{x+7}=16$

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.

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