Log4 8 = simplify using properties of logarithm

Question

Mathematics

Lowery

3 January, 22:32

Log4 8 = simplify using properties of logarithm

+4

Answers (2)

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Sylvia Kane · Answer 1

Using logarithm property,

log4 (8) = log10 (8) / log10 (4)

= log10 (2) ^3 / log10 (2) ^2

= 3*log10 (2) / 2*log10 (2)

= 3/2

= 1.5

Clara Ball · Answer 2

8 = (2) cubed.

So log (8) in any base = 3 log (2) in the same base.

But 2 is the square root of 4, so in the base of 4, log₄ (2) = 1/2

log₄ (8) = 3 log₄ (2) = 3 x 1/2 = 1.5