Solve for x 3=10^x

$3 = 10^{x}$

Step 1

Rewrite the equation as $10^{x} = 3$ .

$10^{x} = 3$

Step 2

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{x}) = \log (3)$

Step 3

Expand the left side.

Expand $\log (10^{x})$ by moving $x$ outside the logarithm.

$x \log (10) = \log (3)$

Logarithm base $10$ of $10$ is $1$ .

$x \cdot 1 = \log (3)$

Multiply $x$ by $1$ .

$x = \log (3)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \log (3)$

Decimal Form:

$x = 0.47712125 \dots$