Trigonometry Examples

$\log (x + 3) \cdot 25 = 2$

Step 1

Divide each term in $\log (x + 3) \cdot 25 = 2$ by $25$ and simplify.

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Step 1.1

Divide each term in $\log (x + 3) \cdot 25 = 2$ by $25$ .

$\frac{\log (x + 3) \cdot 25}{25} = \frac{2}{25}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $25$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{\log (x + 3) \cdot 25}{25} = \frac{2}{25}$

Step 1.2.1.2

Divide $\log (x + 3)$ by $1$ .

$\log (x + 3) = \frac{2}{25}$

Step 2

Rewrite $\log (x + 3) = \frac{2}{25}$ 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 $b^{y} = x$ .

$10^{\frac{2}{25}} = x + 3$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $x + 3 = 10^{\frac{2}{25}}$ .

$x + 3 = 10^{\frac{2}{25}}$

Step 3.2

Subtract $3$ from both sides of the equation.

$x = 10^{\frac{2}{25}} - 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 10^{\frac{2}{25}} - 3$

Decimal Form:

$x = - 1.79773556 \dots$