Finite Math Examples

$3 (5^{x}) - 8 = 0$

Step 1

Multiply $3$ by $5^{x}$ .

$3 \cdot 5^{x} - 8 = 0$

Step 2

Add $8$ to both sides of the equation.

$3 \cdot 5^{x} = 8$

Step 3

Divide each term in $3 \cdot 5^{x} = 8$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 \cdot 5^{x} = 8$ by $3$ .

$\frac{3 \cdot 5^{x}}{3} = \frac{8}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 \cdot 5^{x}}{3} = \frac{8}{3}$

Step 3.2.1.2

Divide $5^{x}$ by $1$ .

$5^{x} = \frac{8}{3}$

Step 4

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

$\ln (5^{x}) = \ln (\frac{8}{3})$

Step 5

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

$x \ln (5) = \ln (\frac{8}{3})$

Step 6

Divide each term in $x \ln (5) = \ln (\frac{8}{3})$ by $\ln (5)$ and simplify.

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Step 6.1

Divide each term in $x \ln (5) = \ln (\frac{8}{3})$ by $\ln (5)$ .

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (\frac{8}{3})}{\ln (5)}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $\ln (5)$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (\frac{8}{3})}{\ln (5)}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{8}{3})}{\ln (5)}$