Basic Math Examples

$7^{5 v} + 5 = 37$

Step 1

Move all terms not containing $v$ to the right side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

$7^{5 v} = 37 - 5$

Step 1.2

Subtract $5$ from $37$ .

$7^{5 v} = 32$

Step 2

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

$\ln (7^{5 v}) = \ln (32)$

Step 3

Expand $\ln (7^{5 v})$ by moving $5 v$ outside the logarithm.

$5 v \ln (7) = \ln (32)$

Step 4

Divide each term in $5 v \ln (7) = \ln (32)$ by $5 \ln (7)$ and simplify.

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Step 4.1

Divide each term in $5 v \ln (7) = \ln (32)$ by $5 \ln (7)$ .

$\frac{5 v \ln (7)}{5 \ln (7)} = \frac{\ln (32)}{5 \ln (7)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 v \ln (7)}{5 \ln (7)} = \frac{\ln (32)}{5 \ln (7)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{v \ln (7)}{\ln (7)} = \frac{\ln (32)}{5 \ln (7)}$

Step 4.2.2

Cancel the common factor of $\ln (7)$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{v \ln (7)}{\ln (7)} = \frac{\ln (32)}{5 \ln (7)}$

Step 4.2.2.2

Divide $v$ by $1$ .

$v = \frac{\ln (32)}{5 \ln (7)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = \frac{\ln (32)}{5 \ln (7)}$

Decimal Form:

$v = 0.35620718 \dots$