SOLUTION: Pg 560 62. Express as a single logarithm with a coefficient of 1. (The "b"s are tiny and below "log") 2 logbx-3(logby+logbz)

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Question 201176This question is from textbook intermediate algebra
: Pg 560
62. Express as a single logarithm with a coefficient of 1.
(The "b"s are tiny and below "log")
2 logbx-3(logby+logbz)
This question is from textbook intermediate algebra

Found 2 solutions by RAY100, jim_thompson5910:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
2log(b) x -3( log(b) y + log(b) z
.
remember a log c = logc^a
.
log(b)x^2 -log(b)y^3 -log(b)z^3
.
remember log a +log b = log(a*b),,,and log a -log b =log(a/b)
.
log(b) { x^2 / y^3 * z^3 }
.
checking, let b=10,,, a=1, ,, b=2,,,c=3
.
original eqn = -2.33,,,,answer = -2.33,,,,,ok

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Alog%28b%2C%28x%29%29-3%28log%28b%2C%28y%29%29%2Blog%28b%2C%28z%29%29%29 Start with the given expression.


2%2Alog%28b%2C%28x%29%29-3%2Alog%28b%2C%28y%29%29-3%2Alog%28b%2C%28z%29%29 Distribute


log%28b%2C%28x%5E2%29%29-log%28b%2C%28y%5E3%29%29-log%28b%2C%28z%5E3%29%29 Rewrite the logs using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%28b%2C%28x%5E2%29%29-%28log%28b%2C%28y%5E3%29%29%2Blog%28b%2C%28z%5E3%29%29%29 Factor out a negative from the last two terms.


log%28b%2C%28x%5E2%29%29-log%28b%2C%28y%5E3z%5E3%29%29 Combine the last two logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


log%28b%2C%28%28x%5E2%29%2F%28y%5E3z%5E3%29%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


So