Precalculus Examples

$6 (4^{x}) = 7$

Step 1

Divide each term in $6 \cdot 4^{x} = 7$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 \cdot 4^{x} = 7$ by $6$ .

$\frac{6 \cdot 4^{x}}{6} = \frac{7}{6}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 \cdot 4^{x}}{6} = \frac{7}{6}$

Step 1.2.1.2

Divide $4^{x}$ by $1$ .

$4^{x} = \frac{7}{6}$

Step 2

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

$\ln (4^{x}) = \ln (\frac{7}{6})$

Step 3

Expand $\ln (4^{x})$ by moving $x$ outside the logarithm.

$x \ln (4) = \ln (\frac{7}{6})$

Step 4

Divide each term in $x \ln (4) = \ln (\frac{7}{6})$ by $\ln (4)$ and simplify.

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Step 4.1

Divide each term in $x \ln (4) = \ln (\frac{7}{6})$ by $\ln (4)$ .

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (\frac{7}{6})}{\ln (4)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $\ln (4)$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (\frac{7}{6})}{\ln (4)}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{7}{6})}{\ln (4)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{7}{6})}{\ln (4)}$

Decimal Form:

$x = 0.11119621 \dots$