SOLUTION: The question asks: {{{ log( 2, 3) }}} � {{{ 2log( 2, 4) }}} + {{{ 3log ( 2, 3)}}} The homework needs me to show the steps. Can anyone help? Thanks in advance...

Question 618078: The question asks:
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The homework needs me to show the steps. Can anyone help?
Thanks in advance...
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

I assume the problem is to rewrite this expression as a single logarithm. (Please include the problem's directions in the future.)

The first and last logs are like terms (same base, same argument). So we can add them:

The remaining terms are not like terms. But there are some properties of logarithms that provide another way to combine terms:

These properties require logs of the same base ... with coefficients of 1. Our logs have the same base but they do not have coefficients of 1.

Fortunately there is yet another property of logarithms, , which allows us to "move" a coefficient into the argument as its exponent. Using this property on our logs:

which simplifies to:

Now we can use one of the earlier properties to combine the two logs. We use the second one because its logs, like ours, have a "-" between them:

The fraction does not reduce so, unless you want a mixed number or decimal for 81/16, we are finished.
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