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3 votes
1/3log125/8-2log2/5+log80/125


(1)/(3) log( (125)/(8) ) - 2 log( (2)/(5) ) + log( (80)/(125) )


User Vimukthi
by
8.2k points

1 Answer

6 votes

Answer:


3log2

Explanation:

Given


(1)/(3) log( (125)/(8) ) - 2 log( (2)/(5) ) + log( (80)/(125) )

Required

Solve

Apply logarithm rules


log( \frac{125^{(1)/(3)}}{8^{(1)/(3)}} )- log( (2^2)/(5^2) ) + log( (80)/(125) )


log( (5)/(2)} )- log( (4)/(25) ) + log( (80)/(125) )

Apply quotient rule


log( (5)/(2) / (4)/(25) ) + log( (80)/(125) )


log( (5)/(2) * (25)/(4) ) + log( (80)/(125) )


log( (100)/(8) ) + log( (80)/(125) )

Apply product rule


log( (100*80)/(8*125) )


log( (8000)/(1000) )


log(8)

Express 8 as 2^3


log(2^3)


3log2

User Nfernandez
by
7.9k points

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