Finite Math Examples

$3^{5 x} - 4 = 9$

Step 1

Subtract $9$ from both sides of the equation.

$3^{5 x} - 4 - 9 = 0$

Step 2

Subtract $9$ from $- 4$ .

$3^{5 x} - 13 = 0$

Step 3

Add $13$ to both sides of the equation.

$3^{5 x} = 13$

Step 4

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

$\ln (3^{5 x}) = \ln (13)$

Step 5

Expand $\ln (3^{5 x})$ by moving $5 x$ outside the logarithm.

$5 x \ln (3) = \ln (13)$

Step 6

Divide each term in $5 x \ln (3) = \ln (13)$ by $5 \ln (3)$ and simplify.

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Step 6.1

Divide each term in $5 x \ln (3) = \ln (13)$ by $5 \ln (3)$ .

$\frac{5 x \ln (3)}{5 \ln (3)} = \frac{\ln (13)}{5 \ln (3)}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x \ln (3)}{5 \ln (3)} = \frac{\ln (13)}{5 \ln (3)}$

Step 6.2.1.2

Rewrite the expression.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (13)}{5 \ln (3)}$

Step 6.2.2

Cancel the common factor of $\ln (3)$ .

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Step 6.2.2.1

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (13)}{5 \ln (3)}$

Step 6.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (13)}{5 \ln (3)}$

Step 7

Simplify $\frac{\ln (13)}{5 \ln (3)}$ .

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Step 7.1

Simplify $5 \ln (3)$ by moving $5$ inside the logarithm.

$x = \frac{\ln (13)}{\ln (3^{5})}$

Step 7.2

Raise $3$ to the power of $5$ .

$x = \frac{\ln (13)}{\ln (243)}$