What is the answer to log_{2-3k}(125)=3 ?

The answer to log_{2-3k}(125)=3 is k=-1

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log_{2-3k}(125)=3

lo g_{2 - 3 k} (125) = 3

k = - 1

Solution steps

lo g_{2 - 3 k} (125) = 3

Apply log rules

\frac{1}{lo g _{125} ( 2 - 3 k )} = 3

Multiply both sides by

lo g_{125} (2 - 3 k)

\frac{1}{lo g _{125} ( 2 - 3 k )} lo g_{125} (2 - 3 k) = 3 lo g_{125} (2 - 3 k)

Simplify

1 = 3 lo g_{125} (2 - 3 k)

Switch sides

3 lo g_{125} (2 - 3 k) = 1

Divide both sides by

3

lo g_{125} (2 - 3 k) = \frac{1}{3}

Apply log rules

2 - 3 k = 5

Solve

2 - 3 k = 5 : k = - 1

k = - 1

Verify Solutions:

k = - 1

True

The solution is

k = - 1

lo g_{2} (y + 2) - lo g_{2} (y - 2) = 1

4 ln (x + 6) = - 8

lo g_{3} (x + a) = b

lo g_{3} (4 x - 5) - lo g_{3} (x + 2) = 1

lo g_{3} (x - 9) = x

What is the answer to log_{2-3k}(125)=3 ?
The answer to log_{2-3k}(125)=3 is k=-1
Solve for k: log_{2-3k}(125)=3
The solution is k=-1