Question

log (128/625) expand the following

Answer 1

log128-log625
log2power7-log5power4
7log2-4log5

Answer 2

Given : log₁₀(128/625)

To Find : Value

Solution:

log₁₀(128/625)

= log₁₀128 - log₁₀625

= log₁₀2⁷ - log₁₀5⁴

= 7 log₁₀2 - 4 log₁₀5

= 7 log₁₀2 - 4 log₁₀(10/2)

= 7 log₁₀2 - 4 (log₁₀10 -   log₁₀2)

= 7 log₁₀2 - 4 log₁₀10 + 4log₁₀2

= 11 log₁₀2 - 4 (1)   (  log₁₀10 = 1)

= 11 log₁₀2  - 4

= 11(0.301) - 4    ( log₁₀2 =0.310)

= 3.311 - 4

= -0.689

log₁₀128 - log₁₀625 = -0.689

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