00:01
This problem wants us to write the expression as a single logarithm, and the expression we're given with multiple logs is 3 times log base 7 of w plus 4 times in parentheses log base 7 of z minus 3 times log base 7 of x.
00:14
And to condense this, or to get this expression to a single logarithm, we are going to condense these logarithms together.
00:21
And our first thing we're going to do is take all of our coefficients and eventually write them as the exponent of our logarithm.
00:28
So for our first logarithm, we'll take 3 and make it the exponent of w.
00:33
And then for our two logarithms inside the parentheses, we're going to distribute 4 first to get all of our coefficients taken care of.
00:40
So that will be 4 log base 7 of z minus 4 times 3, or minus 12 log base 7 of x.
00:48
And then within our parentheses now, we are adding, so we can just drop our parentheses because there's nothing left to distribute, not even a negative.
00:56
And now we can take our coefficients and write them as the exponents of our arguments...
