Trigonometry Examples

$10^{5 x - 2} = 73$

Step 1

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{5 x - 2}) = \log (73)$

Step 2

Expand the left side.

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Step 2.1

Expand $\log (10^{5 x - 2})$ by moving $5 x - 2$ outside the logarithm.

$(5 x - 2) \log (10) = \log (73)$

Step 2.2

Logarithm base $10$ of $10$ is $1$ .

$(5 x - 2) \cdot 1 = \log (73)$

Step 2.3

Multiply $5 x - 2$ by $1$ .

$5 x - 2 = \log (73)$

Step 3

Add $2$ to both sides of the equation.

$5 x = \log (73) + 2$

Step 4

Divide each term in $5 x = \log (73) + 2$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x = \log (73) + 2$ by $5$ .

$\frac{5 x}{5} = \frac{\log (73)}{5} + \frac{2}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\log (73)}{5} + \frac{2}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\log (73)}{5} + \frac{2}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\log (73)}{5} + \frac{2}{5}$

Decimal Form:

$x = 0.77266457 \dots$