Solve for x log base 2 of 5x=4

$\log_{2} (5 x) = 4$

Step 1

Rewrite $\log_{2} (5 x) = 4$ 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 $b^{y} = x$ .

$2^{4} = 5 x$

Step 2

Solve for $x$ .

Rewrite the equation as $5 x = 2^{4}$ .

$5 x = 2^{4}$

Divide each term in $5 x = 2^{4}$ by $5$ and simplify.

Divide each term in $5 x = 2^{4}$ by $5$ .

$\frac{5 x}{5} = \frac{2^{4}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{2^{4}}{5}$

Divide $x$ by $1$ .

$x = \frac{2^{4}}{5}$

Simplify the right side.

Raise $2$ to the power of $4$ .

$x = \frac{16}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{16}{5}$

Decimal Form:

$x = 3.2$

Mixed Number Form:

$x = 3 \frac{1}{5}$

Solve for x log base 2 of 5x=4

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