Solve the logarithmic equation: log_x 103 = 3

Question

ScanSolve AI Tutor · Accepted Answer

let's solve this logarithmic equation.

Given the equation:

\log_x 10^3 = 3

Simplify the term $10^3$ .
$\log_x 1000 = 3$
Convert the logarithmic equation into its equivalent exponential form.
The definition of a logarithm states that $\log_b a = c$ is equivalent to $b^c = a$ .
Applying this to our equation, where $b=x$ , $a=1000$ , and $c=3$ :
$x^3 = 1000$
Solve for $x$ by taking the cube root of both sides.
$x = \sqrt[3]{1000}$ $x = 10$
Check the validity of the solution.
For a logarithm $\log_b a$ , the base $b$ must be positive and $b \neq 1$ . Our solution $x=10$ satisfies these conditions ( $10 > 0$ and $10 \neq 1$ ).

The value of $x$ is $\boxed{10}$ .

Answer