Basic Math Examples

$7^{0.3 x} = 813$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (7^{0.3 x}) = \ln (813)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (7^{0.3 x})$ by moving $0.3 x$ outside the logarithm.

$0.3 x \ln (7) = \ln (813)$

Step 2.2

Multiply $\ln (7)$ by $0.3$ .

$0.58377304 x = \ln (813)$

Step 3

Divide each term in $0.58377304 x = \ln (813)$ by $0.58377304$ and simplify.

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Step 3.1

Divide each term in $0.58377304 x = \ln (813)$ by $0.58377304$ .

$\frac{0.58377304 x}{0.58377304} = \frac{\ln (813)}{0.58377304}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.58377304$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.58377304 x}{0.58377304} = \frac{\ln (813)}{0.58377304}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (813)}{0.58377304}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (813)}{0.58377304}$

Step 3.3.2

Log base $2.71828182$ of $813$ is approximately $6.7007311$ .

$x = \frac{6.7007311}{0.58377304}$

Step 3.3.3

Divide $6.7007311$ by $0.58377304$ .

$x = 11.47831536$