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Intermediate Algebra please help?
Write the expression as a sum and/or differerence of multiple of logarithms,
1. In(ex^2/ysquare root z
2.log(100x^2z)
Write the expression as a single logarithm with coefficent 1.
1. 1/2logx-logy+3log(x-3)
2.log2(x^2-5x+6)-log2(x^2-4)+log2(x+2)
1 Answer
- 9 years agoFavorite Answer
Some rules of logarithms:
log a*b = log a + log b
log a/b = log a - log b
log a^n = n * log a
So for the third expression you listed: 1/2logx-logy+3log(x-3) let's split it up into three pieces: 1/2logx, logy, and 3log(x-3)
1/2 log x can be written as log x^(0.5)
3 log (x-3) can be written as log (x-3)^3
Recombining, we get:
log x^0.5 - log y + log (x-3)^3
Now, you can apply the rules above:
log [(x^0.5) * (x-3)^3] / y
Similar machinations for the fourth expression.
The first expression you listed does not appear complete/correct. There is a missing ")" and it's not clear where the sqrt(z) goes.....
The second expression can also use the rules:
log (100*x^2z) = log 100 + log x^2z = 2 + (2z * log x)
(Do you see why log 100 was replaced by 2?)
