Solve for x 10* log of 4x=25

$10 \cdot \log (4 x) = 25$

Step 1

Divide each term in $(10 \cdot \log (4 x)) = 25$ by $10$ and simplify.

Divide each term in $(10 \cdot \log (4 x)) = 25$ by $10$ .

$\frac{(10 \cdot \log (4 x))}{10} = \frac{25}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 \cdot \log (4 x)}{10} = \frac{25}{10}$

Divide $\log (4 x)$ by $1$ .

$\log (4 x) = \frac{25}{10}$

Simplify the right side.

Cancel the common factor of $25$ and $10$ .

Factor $5$ out of $25$ .

$\log (4 x) = \frac{5 (5)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\log (4 x) = \frac{5 \cdot 5}{5 \cdot 2}$

Cancel the common factor.

$\log (4 x) = \frac{5 \cdot 5}{5 \cdot 2}$

Rewrite the expression.

$\log (4 x) = \frac{5}{2}$

Step 2

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

$10^{\frac{5}{2}} = 4 x$

Step 3

Solve for $x$ .

Rewrite the equation as $4 x = 10^{\frac{5}{2}}$ .

$4 x = 10^{\frac{5}{2}}$

Divide each term in $4 x = 10^{\frac{5}{2}}$ by $4$ and simplify.

Divide each term in $4 x = 10^{\frac{5}{2}}$ by $4$ .

$\frac{4 x}{4} = \frac{10^{\frac{5}{2}}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{10^{\frac{5}{2}}}{4}$

Divide $x$ by $1$ .

$x = \frac{10^{\frac{5}{2}}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10^{\frac{5}{2}}}{4}$

Decimal Form:

$x = 79.05694150 \dots$

Solve for x 10* log of 4x=25

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