Precalculus Examples

$8 (a) = 27 {(0.1)}^{n - 1}$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Simplify both sides of the equation.

Tap for more steps...

Step 1.1.1

Multiply $8$ by $a$ .

$8 a = 27 {(0.1)}^{n - 1}$

Step 1.1.2

Remove parentheses.

$8 a = 27 \cdot {0.1}^{n - 1}$

Step 1.2

Divide each term in $8 a = 27 \cdot {0.1}^{n - 1}$ by $27$ .

$\frac{8 a}{27} = \frac{27 \cdot {0.1}^{n - 1}}{27}$

Step 1.3

Reduce by cancelling the common factors.

$\frac{8 a}{27} = {0.1}^{n - 1}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(0.1)$ of the left side $(\frac{8 a}{27})$ equals the exponent $(n - 1)$ .

$\log_{0.1} (\frac{8 a}{27}) = n - 1$