SOLUTION: Condense the expression to a single logarithm with a leading coefficient of 1 using the properties of logarithms. 6 {{{ log( 7, (c) ) }}} + {{{ log( 7, (a) )/ 6 }}} + {{{ l

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Condense the expression to a single logarithm with a leading coefficient of 1 using the properties of logarithms. 6 {{{ log( 7, (c) ) }}} + {{{ log( 7, (a) )/ 6 }}} + {{{ l      Log On


   

Question 1129078: Condense the expression to a single logarithm with a leading coefficient of 1 using the properties of logarithms.
6 +log%28+7%2C++%28c%29++%29+ + +log%28+7%2C++%28a%29++%29%2F++6+ + +log%28+7%2C++%28b%29++%29%2F++6+
Found 3 solutions by greenestamps, MathLover1, stanbon:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


a*log(x) = log(x^a)

6%2Alog%287%2C%28c%29%29%2Blog%287%2C%28a%29%29%2F6%2Blog%287%2C%28b%29%29%2F6 =

=

log%287%2C%28%28c%5E6%29%28a%5E%281%2F6%29%29%28b%5E%281%2F6%29%29%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

6log%28+7%2C+%28c%29+%29+%2B++log%28+7%2C+%28a%29%29%2F6++%2B+log%28+7%2C+%28b%29++%29%2F+6+

36log%28+7%2C+%28c%29+%29%2F6+%2B++log%28+7%2C+%28ab%29%29%2F6++

log%28+7%2C+%28c%5E36%29+%29%2F6+%2B++log%28+7%2C+%28ab%29%29%2F6++

+log%28+7%2C+%28abc%5E36%29%29%2F6+



or, you can do it this way

.........change to base 10


log%28%28ab%29%29%2F%286log%287%29%29+%2B+%286log%28c%29%29%2Flog%287%29

log%28%28ab%29%29%2F%286log%287%29%29+%2B+%2836log%28c%29%29%2F%286log%287%29%29

%28log%28%28ab%29%29+%2B+36log%28c%29%29%2F%286log%287%29%29

%28log%28%28ab%29%29+%2B+log%28%28c%5E36%29%29%29%2F%286log%287%29%29

log%28%28abc%5E36%29%29%2F%286log%287%29%29



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Condense the expression to a single logarithm with a leading coefficient of 1 using the properties of logarithms.
6 *log( 7 (c) ) + log( 7, (a) )/ 6 + log( 7, (b) )/ 6
-----
= log7(c^6) + log7(a)^(1/6) + log7(b)^(1/6)
------
= log base7 of[(c^6*(ab)^1/6)]
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Cheers,
Stan H.
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