SOLUTION: Solve for the unknown Logbase1/4 64=n

Question 1202070: Solve for the unknown
Logbase1/4 64=n
Found 3 solutions by math_tutor2020, josgarithmetic, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: n = -3

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Work Shown:

0.25 = 1/4

Change of base formula

Use the log rule log(A^B) = B*log(A)

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Another approach:

Change of base formula

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Another approach:

Convert to exponential form

The bases are both 4, so the exponents must be equal.

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
---------if hard to read, logarithm base one-fourth, of 64 is n.

In exponential form,
-

The same base so the exponents must be equal.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Solve for the unknown Logbase1/4 64=n ----- Converting to EXPONENTIAL form ----- Converting to 4^{- 1} - n = 3 ------- Exponents set equal to each other, since bases are equal

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