Math help. Please respond.

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$Evaluate $\log_{\sqrt{5}} 125\sqrt{5}$.$

Guest Dec 18, 2014

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Best Answer

+23246

+5

Let log_√5125√5 = x

Then write this into exponential notation: √5^x = 125√5

Now, I want to write 125 with a base of √5:

--- first, 125 = 5³

--- also, (√5)² = 5

--- so: 125 = 5³ = [ (√5)² ]³ = (√5)⁶

--- and: 125√5 = (√5)⁶ ·√5 = (√5)⁷

Thus: √5^x = (√5)⁷---> x = 7

geno3141 Dec 18, 2014

1⁺⁰ Answers

+23246

+5

Best Answer

Let log_√5125√5 = x

Then write this into exponential notation: √5^x = 125√5

Now, I want to write 125 with a base of √5:

--- first, 125 = 5³

--- also, (√5)² = 5

--- so: 125 = 5³ = [ (√5)² ]³ = (√5)⁶

--- and: 125√5 = (√5)⁶ ·√5 = (√5)⁷

Thus: √5^x = (√5)⁷---> x = 7

geno3141 Dec 18, 2014

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