SOLUTION: Write the equivalent log equation to: 5^(3x) = 4x-1

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Question 1116082: Write the equivalent log equation to:
5^(3x) = 4x-1
Found 3 solutions by ankor@dixie-net.com, greenestamps, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equivalent log equation to:
5^(3x) = 4x-1
log%28%285%5E%283x%29%29%29+=+log%28%284x-1%29%29
the log equiv of exponents
3x%2Alog%28%285%29%29+=+log%28%284x-1%29%29
3x+=+log%28%284x-1%29%29%2Flog%28%285%29%29
they are not asking to solve for x, just the equation

Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


By the basic definition of logarithms:

a%5Eb+=+c is equivalent to log%28a%2Cc%29=b

To remember this definition, remember that the log is the exponent.

For your example...

5%5E%283x%29+=+4x-1 is equivalent to log%285%2C%284x-1%29%29+=+3x

Note the answer from the other tutor,

3x+=+log%28%284x-1%29%29%2Flog%28%285%29%29

is also correct, demonstrating the very useful change-of-base rule for logarithms:

log%28a%2Cb%29+=+log%28b%29%2Flog%28a%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Write the equivalent log equation to:
5^(3x) = 4x-1
Converting from this form (EXPONENTIAL) to LOGARITHMIC form makes it simply: highlight_green%28matrix%281%2C3%2C+log+%285%2C+%284x+-+1%29%29%2C+%22=%22%2C+3x%29%29

That's it!!