Finite Math Examples

$3^{d} = \frac{4}{1}$

Step 1

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

$\ln (3^{d}) = \ln (\frac{4}{1})$

Step 2

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

$d \ln (3) = \ln (\frac{4}{1})$

Step 3

Simplify the right side.

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Step 3.1

Divide $4$ by $1$ .

$d \ln (3) = \ln (4)$

Step 4

Divide each term in $d \ln (3) = \ln (4)$ by $\ln (3)$ and simplify.

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Step 4.1

Divide each term in $d \ln (3) = \ln (4)$ by $\ln (3)$ .

$\frac{d \ln (3)}{\ln (3)} = \frac{\ln (4)}{\ln (3)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

$\frac{d \ln (3)}{\ln (3)} = \frac{\ln (4)}{\ln (3)}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{\ln (4)}{\ln (3)}$

Step 5