Solve for x log base 2 of 9x-2 log base 2 of 8=1

$\log_{2} (9 x) - 2 \log_{2} (8) = 1$

Step 1

Simplify each term.

Logarithm base $2$ of $8$ is $3$ .

$\log_{2} (9 x) - 2 \cdot 3 = 1$

Multiply $- 2$ by $3$ .

$\log_{2} (9 x) - 6 = 1$

Step 2

Move all terms not containing $\log_{2} (9 x)$ to the right side of the equation.

Add $6$ to both sides of the equation.

$\log_{2} (9 x) = 1 + 6$

Add $1$ and $6$ .

$\log_{2} (9 x) = 7$

Step 3

Rewrite $\log_{2} (9 x) = 7$ 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 $b^{y} = x$ .

$2^{7} = 9 x$

Step 4

Solve for $x$ .

Rewrite the equation as $9 x = 2^{7}$ .

$9 x = 2^{7}$

Divide each term in $9 x = 2^{7}$ by $9$ and simplify.

Divide each term in $9 x = 2^{7}$ by $9$ .

$\frac{9 x}{9} = \frac{2^{7}}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{2^{7}}{9}$

Divide $x$ by $1$ .

$x = \frac{2^{7}}{9}$

Simplify the right side.

Raise $2$ to the power of $7$ .

$x = \frac{128}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{128}{9}$

Decimal Form:

$x = 14.\overline{2}$

Mixed Number Form:

$x = 14 \frac{2}{9}$

Solve for x log base 2 of 9x-2 log base 2 of 8=1

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