Solve for x log of x+ log of 8=2

$\log (x) + \log (8) = 2$

Step 1

Simplify the left side.

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x \cdot 8) = 2$

Move $8$ to the left of $x$ .

$\log (8 x) = 2$

Step 2

Rewrite $\log (8 x) = 2$ 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 $b^{y} = x$ .

$10^{2} = 8 x$

Step 3

Solve for $x$ .

Rewrite the equation as $8 x = 10^{2}$ .

$8 x = 10^{2}$

Divide each term in $8 x = 10^{2}$ by $8$ and simplify.

Divide each term in $8 x = 10^{2}$ by $8$ .

$\frac{8 x}{8} = \frac{10^{2}}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{10^{2}}{8}$

Divide $x$ by $1$ .

$x = \frac{10^{2}}{8}$

Simplify the right side.

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

$x = \frac{100}{8}$

Cancel the common factor of $100$ and $8$ .

Factor $4$ out of $100$ .

$x = \frac{4 (25)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x = \frac{4 \cdot 25}{4 \cdot 2}$

Cancel the common factor.

$x = \frac{4 \cdot 25}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{25}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{2}$

Decimal Form:

$x = 12.5$

Mixed Number Form:

$x = 12 \frac{1}{2}$

Solve for x log of x+ log of 8=2

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