SOLUTION: Solve algebraically for x: log5x-1 4=1/3

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Question 954010: Solve algebraically for x: log5x-1 4=1/3
Found 2 solutions by Frosty7, MathTherapy:
Answer by Frosty7(4) About Me  (Show Source):
You can put this solution on YOUR website!
log_(5x-1) 4 =1/3
(y=b^x)= (x=log_b(y))
Which is (5x-1)^(1/3)=4
(5x-1)^(1/3)= (64)^(1/3) (same as 4)
5x=65 (add 1 to both sides)
∴ x=13 (divide 5 to both sides)
Hope this helps!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Solve algebraically for x: log5x-1 4=1/3


If log+%285x+-+1%2C+4%29+=+1%2F3, then:

log+%285x+-+1%2C+4%29+=+1%2F3 ---------- Logarithmic form

highlight%28highlight%28%285x+-+1%29%5E%281%2F3%29+=+4%29%29 --------- Exponential form

highlight%28highlight%28%285x+-+1%29%5E%28%281%2F3%29+%2A+3%29+=+4%5E3%29%29 ---- Cubing both sides

 

5x – 1 = 64

5x = 64 + 1

5x = 65

x = 65%2F5, or highlight_green%2813%29