SOLUTION: Prove that, 7log16/15+5log25/24+3log81/80=log2.

Question 818767: Prove that, 7log16/15+5log25/24+3log81/80=log2.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Note: In the future please put parentheses around function arguments.

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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