Law of Logs 13

^{Laws of Logarithms}

^{Laws of Logarithms:

1. log}a^{(u
v) = log}a^{(u)
+ log}a^{(v)
{The log of a product equals the sum of the logs.}

2. log}a^{(u/v)
= log}a^{(u)
- log}a^{(v)
{The log of a quotient equals the difference of the logs.}

3. log}a^(u^{^r}^{) = r log}a^(u)

Use the above properties of logarithms to write (¹/₂)[log(x+1) + 2 log(x-1)] + 2log x as the logarithm of a single quantity.

(¹/₂)[log(x+1) + 2 log(x-1)] + 2log x	= (¹/₂)[log(x+1)+ log(x-1)²] + 2log x	Work within the square brackets and use the third law of exponents.
	Show work.	Apply the first law to combine the terms within square brackets into a single log term.

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