What we will be doing is using properties of logarithms (, and/or ) to condense the entire left side into a single logarithm (hopefully log(2)).
We'll start by using the third property to move the coefficients of each log into its argument as its exponent:
Next we can use the first property to combine the three logs:
To make simplifying the argument easier, I am going to rewrite each numerator and denominator in terms of prime factors:
Now we can use the rule to raise each of these fractions to a power:
Using the rule to multiply the numerators and denominators:
The 3's and 5's all cancel out. And we can use the rule to divide the 2's: Check!
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