Precalculus Examples

$3500 = 700 \cdot 2^{8 x}$

Step 1

Subtract $700 \cdot 2^{8 x}$ from both sides of the equation.

$3500 - 700 \cdot 2^{8 x} = 0$

Step 2

Factor $700$ out of $3500 - 700 \cdot 2^{8 x}$ .

Tap for more steps...

Step 2.1

Factor $700$ out of $3500$ .

$700 (5) - 700 \cdot 2^{8 x} = 0$

Step 2.2

Factor $700$ out of $- 700 \cdot 2^{8 x}$ .

$700 (5) + 700 (- 2^{8 x}) = 0$

Step 2.3

Factor $700$ out of $700 (5) + 700 (- 2^{8 x})$ .

$700 (5 - 2^{8 x}) = 0$

Step 3

Divide each term in $700 (5 - 2^{8 x}) = 0$ by $700$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $700 (5 - 2^{8 x}) = 0$ by $700$ .

$\frac{700 (5 - 2^{8 x})}{700} = \frac{0}{700}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $700$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{700 (5 - 2^{8 x})}{700} = \frac{0}{700}$

Step 3.2.1.2

Divide $5 - 2^{8 x}$ by $1$ .

$5 - 2^{8 x} = \frac{0}{700}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $0$ by $700$ .

$5 - 2^{8 x} = 0$

Step 4

Subtract $5$ from both sides of the equation.

$- 2^{8 x} = - 5$

Step 5

Divide each term in $- 2^{8 x} = - 5$ by $- 1$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 2^{8 x} = - 5$ by $- 1$ .

$\frac{- 2^{8 x}}{- 1} = \frac{- 5}{- 1}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{2^{8 x}}{1} = \frac{- 5}{- 1}$

Step 5.2.2

Divide $2^{8 x}$ by $1$ .

$2^{8 x} = \frac{- 5}{- 1}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $- 5$ by $- 1$ .

$2^{8 x} = 5$

Step 6

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

$\ln (2^{8 x}) = \ln (5)$

Step 7

Expand $\ln (2^{8 x})$ by moving $8 x$ outside the logarithm.

$8 x \ln (2) = \ln (5)$

Step 8

Divide each term in $8 x \ln (2) = \ln (5)$ by $8 \ln (2)$ and simplify.

Tap for more steps...

Step 8.1

Divide each term in $8 x \ln (2) = \ln (5)$ by $8 \ln (2)$ .

$\frac{8 x \ln (2)}{8 \ln (2)} = \frac{\ln (5)}{8 \ln (2)}$

Step 8.2

Simplify the left side.

Tap for more steps...

Step 8.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 8.2.1.1

Cancel the common factor.

$\frac{8 x \ln (2)}{8 \ln (2)} = \frac{\ln (5)}{8 \ln (2)}$

Step 8.2.1.2

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (5)}{8 \ln (2)}$

Step 8.2.2

Cancel the common factor of $\ln (2)$ .

Tap for more steps...

Step 8.2.2.1

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (5)}{8 \ln (2)}$

Step 8.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (5)}{8 \ln (2)}$

Step 9

Simplify $\frac{\ln (5)}{8 \ln (2)}$ .

Tap for more steps...

Step 9.1

Simplify $8 \ln (2)$ by moving $8$ inside the logarithm.

$x = \frac{\ln (5)}{\ln (2^{8})}$

Step 9.2

Raise $2$ to the power of $8$ .

$x = \frac{\ln (5)}{\ln (256)}$