Question 262519
we are given three separate problems. Lets take one at a time:
Problem #1: 
{{{3log(5,x) - log(5,4) = log(5,16)}}} 
step 1- use the power rule to bring all coefficients up as exponents. We get
{{{log(5,x^3) - log(5,4) = log(5,16)}}} 
step 2 - using laws of logs if we see log subtraction, that means division, so we get
{{{log(5,x^3/4) = log(5,16)}}} 
step 3 - since both logs are base 5, we can eliminate then and set the rest equal. We get
{{{x^3/4 = 16}}}
step 4 - multiply by 4 to get
{{{x^3 = 64}}}
step 5 - take a cube root to get
{{{x = 4}}}
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problem #2:
{{{(1/3)log(7,64)+(1/2)log(7,121)=log(7,x)}}}
step 1- use the power rule to bring all coefficients up as exponents. We get
{{{log(7,64^(1/3))+log(7,121^(1/2))=log(7,x)}}}
step 2 - using laws of logs if we see log addition, that means multiplication
{{{log(7,64^(1/3)*121^(1/2)) = log(7,x)}}}
step 3 - since both logs are base 7, we can eliminate then and set the rest equal. We get
{{{4*11 = x}}}
So,
{{{x = 44}}}
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problem #3:
Find 
{{{log(3,25)}}} 
given that {{{log(3,5) = 1.465}}}
step 1 - rewrite {{{log(3,25)}}} as {{{log(3,5^2)}}} and using power rules of logs, bring the 2 out front to get
{{{2log(3,5)}}}
step 2 - by substitution, we get
2*1.465 = 2.93