SOLUTION: Solve the logarithmic equation algebraically. Show steps log(64)1/4=x

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Question 689697: Solve the logarithmic equation algebraically. Show steps
log(64)1/4=x

Found 2 solutions by jsmallt9, MathTherapy:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%2864%2C+%281%2F4%29%29=x
The expression on the left represents the exponent for 64 that results in 1/4. If you are really sharp with your exponents you will already know what this exponent is. If not then we can use the change of base formula, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to convert the base 64 log into a log with a different base. This different base should be one that will make it easy to figure out the value of the log. With an argument of 1/4 a base of 4 looks good. Using the change of base formula to change to base 4 logs we get:
log%284%2C+%281%2F4%29%29%2Flog%284%2C+%2864%29%29=x
After checking various powers of 4 you should know what these two logs are. The power of 4 that equals 1/4 is -1 and the power of 4 that equals 64 is 3. So our expression simplifies to:
%28-1%29%2F3

P.S. Look back at the original expression. See if you can understand why
log%2864%2C+%281%2F4%29%29=-1%2F3

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the logarithmic equation algebraically. Show steps
log(64)1/4=x

log+%2864%2C+%281%2F4%29%29+=+x

64%5Ex+=+1%2F4

%284%5E3%29%5Ex+=+4%5E-+1

4%5E%283x%29+=+4%5E-+1

3x = - 1 ------ As bases are the same, so are their exponents

highlight_green%28x+=+-+1%2F3%29

You can do the check!!

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