log(3^x)=log(15)--->now remember that you can pull this x out in front of the logarithm
xlog3=log15--->divide by log3
x=log15/log3
So if you know that logbase4(3)=x, you know that 4^x=3
Now just use exponent rules--->4=2^2, so:
2^2x=3----->now you what the right side to equal 24 because that is what you want the equation to be equal to, so you would have to multiply by 8 on both sides.
2^2x*8=24---->now notice that 8 is also 2^3 b/c 2*2*2=8, so
2^2x*2^3=24---->now since you have a common base, you can combine the two exponents; when you multiply two bases, you add the exponents, so:
2^(2x+3)=24----->now take logbase2 of both sides
logbase2(2^(2x+3))=logbase2(24)--->now you've got logbase2(24) like the question asked, but you can simplify further because you've got an exponent in the logarithm, so pull out front
(2x+3)logbase2(2)=logbase2(24)----->no… logbase2(2) is 1 because it is asking 2 to the ? power equals 2 and so if you raise 2 to the first that equals two, so logbase2(2)=1, so:
(2x+3)(1)=logbase2(24)
2x+3=logbase2(24)