Precalculus Examples

$\ln (2) = 4 t \ln (1.028)$

Step 1

Rewrite the equation as $4 t \ln (1.028) = \ln (2)$ .

$4 t \ln (1.028) = \ln (2)$

Step 2

Divide each term in $4 t \ln (1.028) = \ln (2)$ by $4 \ln (1.028)$ and simplify.

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Step 2.1

Divide each term in $4 t \ln (1.028) = \ln (2)$ by $4 \ln (1.028)$ .

$\frac{4 t \ln (1.028)}{4 \ln (1.028)} = \frac{\ln (2)}{4 \ln (1.028)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 t \ln (1.028)}{4 \ln (1.028)} = \frac{\ln (2)}{4 \ln (1.028)}$

Step 2.2.1.2

Rewrite the expression.

$\frac{t \ln (1.028)}{\ln (1.028)} = \frac{\ln (2)}{4 \ln (1.028)}$

Step 2.2.2

Cancel the common factor of $\ln (1.028)$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{t \ln (1.028)}{\ln (1.028)} = \frac{\ln (2)}{4 \ln (1.028)}$

Step 2.2.2.2

Divide $t$ by $1$ .

$t = \frac{\ln (2)}{4 \ln (1.028)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (2)}{4 \ln (1.028)}$

Decimal Form:

$t = 6.27505873 \dots$