Algebra Examples

$(3^{8}) \cdot 4 = 3^{x}$

Step 1

Rewrite the equation as $3^{x} = 3^{8} \cdot 4$ .

$3^{x} = 3^{8} \cdot 4$

Step 2

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

$\ln (3^{x}) = \ln (3^{8} \cdot 4)$

Step 3

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

$x \ln (3) = \ln (3^{8} \cdot 4)$

Step 4

Simplify the right side.

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Step 4.1

Simplify $\ln (3^{8} \cdot 4)$ .

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Step 4.1.1

Raise $3$ to the power of $8$ .

$x \ln (3) = \ln (6561 \cdot 4)$

Step 4.1.2

Multiply $6561$ by $4$ .

$x \ln (3) = \ln (26244)$

Step 5

Divide each term in $x \ln (3) = \ln (26244)$ by $\ln (3)$ and simplify.

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Step 5.1

Divide each term in $x \ln (3) = \ln (26244)$ by $\ln (3)$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (26244)}{\ln (3)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (3)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (26244)}{\ln (3)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (26244)}{\ln (3)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (26244)}{\ln (3)}$

Decimal Form:

$x = 9.26185950 \dots$