Precalculus Examples

$3 \ln (5) x = 10$

Step 1

Divide each term in $3 \ln (5) x = 10$ by $3 \ln (5)$ .

$\frac{3 \ln (5) x}{3 \ln (5)} = \frac{10}{3 \ln (5)}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{3 \ln (5) x}{3 \ln (5)} = \frac{10}{3 \ln (5)}$

Step 2.1.2

Rewrite the expression.

$\frac{\ln (5) x}{\ln (5)} = \frac{10}{3 \ln (5)}$

Step 2.2

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

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Step 2.2.1

Cancel the common factor.

$\frac{\ln (5) x}{\ln (5)} = \frac{10}{3 \ln (5)}$

Step 2.2.2

Divide $x$ by $1$ .

$x = \frac{10}{3 \ln (5)}$

Step 3

Simplify the right side.

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Step 3.1

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

$x = \frac{10}{\ln (5^{3})}$

Step 3.2

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

$x = \frac{10}{\ln (125)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{\ln (125)}$

Decimal Form:

$x = 2.07111644 \dots$