Precalculus Examples

$3 (2^{x}) = 42$

Step 1

Divide each term in $3 \cdot 2^{x} = 42$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 \cdot 2^{x} = 42$ by $3$ .

$\frac{3 \cdot 2^{x}}{3} = \frac{42}{3}$

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.

$\frac{3 \cdot 2^{x}}{3} = \frac{42}{3}$

Step 1.2.1.2

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

$2^{x} = \frac{42}{3}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $42$ by $3$ .

$2^{x} = 14$

Step 2

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

$\ln (2^{x}) = \ln (14)$

Step 3

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

$x \ln (2) = \ln (14)$

Step 4

Divide each term in $x \ln (2) = \ln (14)$ by $\ln (2)$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $x \ln (2) = \ln (14)$ by $\ln (2)$ .

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (14)}{\ln (2)}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

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

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (14)}{\ln (2)}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (14)}{\ln (2)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (14)}{\ln (2)}$

Decimal Form:

$x = 3.80735492 \dots$