Solve for k log base 8 of 28k-20+15=18

$\log_{8} (28 k - 20) + 15 = 18$

Move all terms not containing $\log_{8} (28 k - 20)$ to the right side of the equation.

Subtract $15$ from both sides of the equation.

$\log_{8} (28 k - 20) = 18 - 15$

Subtract $15$ from $18$ .

$\log_{8} (28 k - 20) = 3$

Rewrite $\log_{8} (28 k - 20) = 3$ 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 $b^{y} = x$ .

$8^{3} = 28 k - 20$

Solve for $k$ .

Rewrite the equation as $28 k - 20 = 8^{3}$ .

$28 k - 20 = 8^{3}$

Raise $8$ to the power of $3$ .

$28 k - 20 = 512$

Move all terms not containing $k$ to the right side of the equation.

Add $20$ to both sides of the equation.

$28 k = 512 + 20$

Add $512$ and $20$ .

$28 k = 532$

Divide each term in $28 k = 532$ by $28$ and simplify.

Divide each term in $28 k = 532$ by $28$ .

$\frac{28 k}{28} = \frac{532}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 k}{28} = \frac{532}{28}$

Divide $k$ by $1$ .

$k = \frac{532}{28}$

Simplify the right side.

Divide $532$ by $28$ .

$k = 19$

Solve for k log base 8 of 28k-20+15=18

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