Finite Math Examples

$\log (2) (\log_{3} (x)) = 4$

Step 1

Divide each term in $\log (2) \log_{3} (x) = 4$ by $\log (2)$ and simplify.

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Step 1.1

Divide each term in $\log (2) \log_{3} (x) = 4$ by $\log (2)$ .

$\frac{\log (2) \log_{3} (x)}{\log (2)} = \frac{4}{\log (2)}$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

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Step 1.2.1.1

Cancel the common factor.

$\frac{\log (2) \log_{3} (x)}{\log (2)} = \frac{4}{\log (2)}$

Step 1.2.1.2

Divide $\log_{3} (x)$ by $1$ .

$\log_{3} (x) = \frac{4}{\log (2)}$

Step 2

Rewrite $\log_{3} (x) = \frac{4}{\log (2)}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$3^{\frac{4}{\log (2)}} = x$

Step 3

Rewrite the equation as $x = 3^{\frac{4}{\log (2)}}$ .

$x = 3^{\frac{4}{\log (2)}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 3^{\frac{4}{\log (2)}}$

Decimal Form:

$x = 2187006.14285749$