Answer
$x = 3$
Work Step by Step
Subtract $8$ from both sides of the equation to isolate the exponential term:
$10^{x} = 1000$
Rewrite the terms so they share a common base (note that $1000=10^3$):
$10^{x} = 10^{3}$
If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $x$:
$x = 3$
Check the answer by substituting $3$ for $x$ in the original equation:
$8 + 10^{3} = 1008$
Subtract $8$ from both sides of the equation:
$10^{3} = 1000$
Evaluate the exponential expression on the left side of the equation:
$1000 = 1000$
Both sides of the equation are equal to one another; therefore, the answer is correct.
