Evaluate 10^(6x)=93

$10^{6 x} = 93$

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

$\log (10^{6 x}) = \log (93)$

Expand the left side.

Expand $\log (10^{6 x})$ by moving $6 x$ outside the logarithm.

$6 x \log (10) = \log (93)$

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

$6 x \cdot 1 = \log (93)$

Multiply $6$ by $1$ .

$6 x = \log (93)$

Divide each term in $6 x = \log (93)$ by $6$ and simplify.

Divide each term in $6 x = \log (93)$ by $6$ .

$\frac{6 x}{6} = \frac{\log (93)}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{\log (93)}{6}$

Divide $x$ by $1$ .

$x = \frac{\log (93)}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\log (93)}{6}$

Decimal Form:

$x = 0.32808049 \dots$