find the exact value

0

1288

2

log5 180 − log5 75 − log5 60

Guest Feb 21, 2016

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Best Answer

+33659

+20

1. Use the fact that log_bx - log_by = log_b(x/y)

log₅180 - log₅75 - log₅60 = log₅(1/25) → log₅(25^-1) → log₅(5^-2)

2. Now use the fact that log_b(b^m) = m

log₅(5^-2) = -2

So log₅180 - log₅75 - log₅60 = -2

.

Alan Feb 21, 2016

2⁺⁰ Answers

+333

0

The exact value is -2.

Misaki Feb 21, 2016

+33659

+20

Best Answer

1. Use the fact that log_bx - log_by = log_b(x/y)

log₅180 - log₅75 - log₅60 = log₅(1/25) → log₅(25^-1) → log₅(5^-2)

2. Now use the fact that log_b(b^m) = m

log₅(5^-2) = -2

So log₅180 - log₅75 - log₅60 = -2

.

Alan Feb 21, 2016

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