Trigonometry Examples

$\log_{2} (3^{x}) = \log_{4} (10)$

Step 1

Expand $\log_{2} (3^{x})$ by moving $x$ outside the logarithm.

$x \log_{2} (3)$

Step 2

The expanded equation is $x \log_{2} (3) = \log_{4} (10)$ .

$x \log_{2} (3) = \log_{4} (10)$

Step 3

Divide each term in $x \log_{2} (3) = \log_{4} (10)$ by $\log_{2} (3)$ and simplify.

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Step 3.1

Divide each term in $x \log_{2} (3) = \log_{4} (10)$ by $\log_{2} (3)$ .

$\frac{x \log_{2} (3)}{\log_{2} (3)} = \frac{\log_{4} (10)}{\log_{2} (3)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\log_{2} (3)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \log_{2} (3)}{\log_{2} (3)} = \frac{\log_{4} (10)}{\log_{2} (3)}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\log_{4} (10)}{\log_{2} (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\log_{4} (10)}{\log_{2} (3)}$

Decimal Form:

$x = 1.04795163 \dots$