Solve for x log of 6x+5=2

$\log (6 x + 5) = 2$

Step 1

Rewrite $\log (6 x + 5) = 2$ 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 $b^{y} = x$ .

$10^{2} = 6 x + 5$

Step 2

Solve for $x$ .

Rewrite the equation as $6 x + 5 = 10^{2}$ .

$6 x + 5 = 10^{2}$

Raise $10$ to the power of $2$ .

$6 x + 5 = 100$

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$6 x = 100 - 5$

Subtract $5$ from $100$ .

$6 x = 95$

Divide each term in $6 x = 95$ by $6$ and simplify.

Divide each term in $6 x = 95$ by $6$ .

$\frac{6 x}{6} = \frac{95}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{95}{6}$

Divide $x$ by $1$ .

$x = \frac{95}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{95}{6}$

Decimal Form:

$x = 15.8\overline{3}$

Mixed Number Form:

$x = 15 \frac{5}{6}$

Solve for x log of 6x+5=2

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