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when expanding a logarithm when two terms are being multiplied together the sum of the logarithm of the two taken seperately is equal for example log base 5 of x(y) is equal to log base 5 of x + log base 5 of y
when a term is being divided then you use the difference of the log with the same base for example log base 5 of x/y is equal to log base 5 of x - log base 5 of y
does that help?
\[\log5 y(x+2)/x^4 = \log5 y(x+2) - \log5x^4 = \log5y+\log5(x+2) - 4\log5x\]
im so lost
bubbamurphy your answer gets cut off
Sorry the above reply got cut out. \[\log5y(x+2) - \log5x^4 = \log5y + \log5(x+2) - 4\log5x\]
The righthand side of that last post should be your final answer (assuming by log5 you meant base 5)
and yes then you move the power to the front
as bubbamurphy did
when two or multiple things are being multiplied together in the same log you can separate them with addition when they are being divided then you may use subtraction
i did thankyou
-4log5x is my answer?
the whole left side of the equation that bubbamurphy posted is your completed answer
no thankyou allot
no problem any other questions while i am here?
expand the expression: log3(x^-2y^3)
\[\log3(x^(-2y^3) = -2y^3\log3x\]
what is above the first x?
the way that you wrote the problem x was to the power of -2y^3
so if x is to the power of that entire quantity you can move that quantity to the front of the logarithm
quantity meaning -2y^3
that is a parenthesis above the first x
there should be a end parenthesis after the -2y^3
thankyou for your help
No problem. :)
do you have time for more?