Question

The equation. Check for extran solutions. log_(8)(28x-20)+15=18

Answer 1

The solution to the equation
`log_(8`)(28x-20)+15=18 is x = 27/28.

Step-by-step explanation:

To solve the equation

`log_(8)`(28x-20)+15=18,

we start by isolating the logarithmic term. Subtracting 15 from both sides gives

`log_(8)`(28x-20) = 3.

To remove the logarithm, rewrite the equation in exponential form:

8³ = 28x-20.

Solving for x, we get

28x = 512 + 20

which simplifies to

28x = 532.

Finally, divide both sides by 28 to find

x = 532/28 = 27/28.

This solution satisfies the original equation as

`log_(8)`(28 * (27/28) - 20) + 15 =
`log_(8)`(27 - 20) + 15 =
`log_(8)`(7) + 15. Applying the logarithm properties

`log_(8)`(7) = 3, so 3 + 15 = 18

confirming the validity of

x = 27/28.