SOLUTION: log27^x=4/3

Question 64195: log27^x=4/3
Answer by burkus(4) (Show Source): You can put this solution on YOUR website!
This is a tricky log problem. The best thing to do with logs is to actually raise both sides to a power. This eliminates the log part of the equation.
If you raise both sides to a power of logx = 5, for example you would get x = 10^5.
So for your problem, you would raise both sides by the power of 27.
log27^x=4/3 becomes
27 ^ ( log 27^x ) = 27 ^ ( 4/3) (read 27 to the 4/3 power)
Keep in mind that 27 is 3 cubed. That's 3 to the 3 power.
( 3 * 4 / 3 ) The quantity 3 times 4 /3 = 4.
so the right side above, copied below is
= = (because the 3's cancel in the exponent part of the equation (the upper)
What is ?
3 times 3 times 3 times 3
Answer is 27 * 3.
or 81.

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