Use the Laws of logarithms to rewrite the expression
log ( x 2 y 10 z 2 ) \displaystyle {\log{{\left({\frac{{{x}^{{{2}}}{y}^{{{10}}}}}{{{z}^{{{2}}}}}}\right)}}} log ( z 2 x 2 y 10 )
in a form with no logarithm of a product, quotient or power.
After rewriting we have
log ( x 2 y 10 z 2 ) = A log ( x ) + B log ( y ) + C log ( z ) \displaystyle {\log{{\left({\frac{{{x}^{{{2}}}{y}^{{{10}}}}}{{{z}^{{{2}}}}}}\right)}}}={A}{\log{{\left({x}\right)}}}+{B}{\log{{\left({y}\right)}}}+{C}{\log{{\left({z}\right)}}} log ( z 2 x 2 y 10 ) = A log ( x ) + B log ( y ) + C log ( z )
with
A = \displaystyle {A}= A = Preview Question 6 Part 1 of 3 B = \displaystyle {B}= B = Preview Question 6 Part 2 of 3
and
C = \displaystyle {C}= C = Preview Question 6 Part 3 of 3 Submit Try a similar question
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Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)