Question

Evaluate log2 1/8.

Answer 1

\[\log_{2}\frac{1}{8}= x \]

Answer 2

What is the base?

Answer 3

2?

Answer 4

What is the exponent?

Answer 5

x

Answer 6

So we have:
\[2^x\]

Answer 7

What does that equal?

Answer 8

2^x=1/8?

Answer 9

Now replace 8 with a power of 2

Answer 10

8 = 2^?

Answer 11

@Tomo Let the asker answer the questions.

Answer 12

ok, yes, i was trying to help the user understand the following concept

\[\ln_x{x^y} = y*\ln_x{x} = y*1 = 1\]

Answer 13

2^x=2^3?

Answer 14

\[2^x=\frac{1}{2^3}\]

Answer 15

Now move the 2^3 to the numerator

Answer 16

2^x=-2^3?

Answer 17

\[2^x=2^{-3}\]

Answer 18

The bases are the same, the expressions are equal so the exponents must be equal.

Answer 19

So for log5 1/125, x=-3?

Answer 20

yes. Good for you!!

Answer 21

Thank you!

Answer 22

yw