Math CentralQuandaries & Queries


Question from motaz, a student:

Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x

Hi Motaz. Let me demonstrate with a similar question:

Let z = log5 (1/625).

Start by realizing that if the log is in base 5, we want to exponentiate with base 5 on both sides:

5z = 5 log5 (1/625)

On the right hand side, the exponentiation and the log cancel each other, because they have the same base of 5. So this simplifies to

5z = 1/625

From here, it is just normal work with exponents:

5z = 625-1
5z = (252)-1
5z = [(52)2]-1
5z = 5-4
z = -4.

Now you can do your question exactly the same way.

Stephen La Rocque.

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