SOLUTION: Could someone please help me with this? Rewrite as a single logarithm: alog x-blog y-clog z. first space between g & x on problem there is a little 3 but my computer will not

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Could someone please help me with this? Rewrite as a single logarithm: alog x-blog y-clog z. first space between g & x on problem there is a little 3 but my computer will not       Log On


   

Question 82436: Could someone please help me with this?
Rewrite as a single logarithm:
alog x-blog y-clog z.
first space between g & x on problem there is a little 3 but my computer will not allow the function. It sets a little below the letters. It is the same number (3) between g & Y, and g & Z.
Found 2 solutions by Earlsdon, scott8148:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite as a single logarithm:
aLog%5B3%5D%28x%29-bLog%5B3%5D%28y%29-cLog%5B3%5D%28z%29 Apply the "power rule" for logarithms:Log%5Bb%5DM%5Ep+=+pLog%5Bb%5DM
Log%5B3%5Dx%5Ea+-+Log%5B3%5Dy%5Eb+-+Log%5B3%5Dz%5Ec Now apply the "quotient rule" for logarithms:Log%5Bb%5DM+-+Log%5Bb%5DN+=+Log%5Bb%5D%28M%2FN%29
Log%5B3%5D%28x%5Ea%2Fy%5Eb%29+-+Log%5B3%5Dz%5Ec Apply the quotient rule once more.
Log%5B3%5D%28%28x%5Ea%2Fy%5Eb%29%2Fz%5Ec%29 Simplify.
Log%5B3%5D%28x%5Ea%2F%28y%5Eb%2Az%5Ec%29%29

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the 3, written as a subscript, means that 3 is the base of the logs ... logarithms are just exponents that the base is raised to in order to get the desired value ... the log of 9 in base 3 is 2 because 3 to the second power is 9 ... log3(9)=2 ... subtracting logs (exponents) is the same as dividing numbers ... multiplying logs is the same as raising to a power

alog3(x)-blog3(y)-clog3(z) ... log3%28%28x%5Ea%29%2F%28%28y%5Eb%29%28z%5Ec%29%29%29