Solve for x log base 3 of 5x=2

$\log_{3} (5 x) = 2$

Step 1

Rewrite $\log_{3} (5 x) = 2$ 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 $b^{y} = x$ .

$3^{2} = 5 x$

Step 2

Solve for $x$ .

Rewrite the equation as $5 x = 3^{2}$ .

$5 x = 3^{2}$

Divide each term in $5 x = 3^{2}$ by $5$ and simplify.

Divide each term in $5 x = 3^{2}$ by $5$ .

$\frac{5 x}{5} = \frac{3^{2}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{3^{2}}{5}$

Divide $x$ by $1$ .

$x = \frac{3^{2}}{5}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$x = \frac{9}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{5}$

Decimal Form:

$x = 1.8$

Mixed Number Form:

$x = 1 \frac{4}{5}$

Solve for x log base 3 of 5x=2

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