How do you solve #Log_b 64 = 6#?

Answer 1

#b^6=64->b^6 = 2^6->(b^6)^(1/6) = (2^6)^(1/6) ->b = 2# Or
#b^6=64->root6(b^6) =root6(64)->b=2#

First, use definition of logarithm to change to exponential form then solve for b by taking the sixth root of both sides.

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Answer 2

Sophie Adams

To solve (\log_b 64 = 6), you need to rewrite the equation in exponential form.

The base (b) raised to the power of the logarithm equals the number inside the logarithm.

So, (b^6 = 64).

To find the value of (b), you need to determine what number raised to the power of 6 equals 64.

(b^6 = 64)

Taking the sixth root of both sides gives:

(b = \sqrt[6]{64})

(b = 2)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.