SOLUTION: Solve the equation 3log[base5]x - log[base5]4 = log[base5]16. Solve the equation 1/3log[base7]64+1/2log[base7]121=log[base7]x Find log[base3]25 given that log[base3]5 = 1.465

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Question 262519: Solve the equation 3log[base5]x - log[base5]4 = log[base5]16.
Solve the equation 1/3log[base7]64+1/2log[base7]121=log[base7]x
Find log[base3]25 given that log[base3]5 = 1.465
Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
we are given three separate problems. Lets take one at a time:
Problem #1:

step 1- use the power rule to bring all coefficients up as exponents. We get

step 2 - using laws of logs if we see log subtraction, that means division, so we get

step 3 - since both logs are base 5, we can eliminate then and set the rest equal. We get

step 4 - multiply by 4 to get

step 5 - take a cube root to get

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problem #2:

step 1- use the power rule to bring all coefficients up as exponents. We get

step 2 - using laws of logs if we see log addition, that means multiplication

step 3 - since both logs are base 7, we can eliminate then and set the rest equal. We get

So,

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problem #3:
Find

given that
step 1 - rewrite as and using power rules of logs, bring the 2 out front to get

step 2 - by substitution, we get
2*1.465 = 2.93