Precalculus Examples

$3 {(1.04)}^{3 t} = 8$

Step 1

Divide each term in $3 \cdot {1.04}^{3 t} = 8$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 \cdot {1.04}^{3 t} = 8$ by $3$ .

$\frac{3 \cdot {1.04}^{3 t}}{3} = \frac{8}{3}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 \cdot {1.04}^{3 t}}{3} = \frac{8}{3}$

Step 1.2.1.2

Divide ${1.04}^{3 t}$ by $1$ .

${1.04}^{3 t} = \frac{8}{3}$

Step 2

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

$\ln ({1.04}^{3 t}) = \ln (\frac{8}{3})$

Step 3

Expand $\ln ({1.04}^{3 t})$ by moving $3 t$ outside the logarithm.

$3 t \ln (1.04) = \ln (\frac{8}{3})$

Step 4

Divide each term in $3 t \ln (1.04) = \ln (\frac{8}{3})$ by $3 \ln (1.04)$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $3 t \ln (1.04) = \ln (\frac{8}{3})$ by $3 \ln (1.04)$ .

$\frac{3 t \ln (1.04)}{3 \ln (1.04)} = \frac{\ln (\frac{8}{3})}{3 \ln (1.04)}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{3 t \ln (1.04)}{3 \ln (1.04)} = \frac{\ln (\frac{8}{3})}{3 \ln (1.04)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{t \ln (1.04)}{\ln (1.04)} = \frac{\ln (\frac{8}{3})}{3 \ln (1.04)}$

Step 4.2.2

Cancel the common factor of $\ln (1.04)$ .

Tap for more steps...

Step 4.2.2.1

Cancel the common factor.

$\frac{t \ln (1.04)}{\ln (1.04)} = \frac{\ln (\frac{8}{3})}{3 \ln (1.04)}$

Step 4.2.2.2

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{8}{3})}{3 \ln (1.04)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (\frac{8}{3})}{3 \ln (1.04)}$

Decimal Form:

$t = 8.33598009 \dots$