Question 139884: sample final questions:
write as a single logarithm expression: have no clue how to start:
(#1) -2logbase3(1/x)+1/3logbase3(squa rt OF x)
(#2) 2log2-3logx-1/2[log(x+3)log(x-2)]
express as sum & difference of logarithms, express powers as factors:
(#3) ln(x^3sqrtx^2+1 /x-3)
solve each equation:
(#4) log(7x+8)=2logx
THANK YOU AND GOD BLESS....THIS IS HELPING ME STUDY WITH THE CORRECT METHOD AND ANSWER.....I TRULY APPRECIATE ALL YOUR HELP AS ALWAYS!!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (#1) -2logbase3(1/x)+1/3logbase3(squa rt OF x)
= -2log3 (x^-1) + (1/3)log3 x^(1/2)
= (-1)(-2)log3 x + (1/2)(1/3)log3 x
= 2log3 x + (1/6) log3 x
= (13/6)log3 x
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(#2) 2log2-3logx-1/2[log(x+3)log(x-2)]
= 2log2 - logx -(1/2)[log(x+3)log(x-2)]
= log(4/x) -(1/2)log(x+3)*log(x-2)
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express as sum & difference of logarithms, express powers as factors:
(#3) ln(x^3sqrt[(x^2+1)/(x-3)]
= 3lnx + (1/2)ln[(x^2+1)/(x-3)]
-----------------------------------------
solve each equation:
(#4) log(7x+8)=2logx
log(7x+8) = log x^2
7x+8 = x^2
x^2-7x-8 = 0
(x-8)(x+1) = 0
Potitive solution:
x = 8
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Cheers,
Stan H.
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