SOLUTION: Please help I am stuck on this problem. Round to the nearest thousandth log5(5z/z-2) = 2

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Question 890998: Please help I am stuck on this problem.
Round to the nearest thousandth
log5(5z/z-2) = 2
Found 3 solutions by Tatiana_Stebko, josgarithmetic, MathTherapy:
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C%28%285z%2F%28z-2%29%29%29%29=2

Change Of Base seems to be the best method first.

log%2810%2C%28%285z%2F%28z-2%29%29%29%29%2Flog%2810%2C5%29=2

log%2810%2C%28%285z%2F%28z-2%29%29%29%29=2%2Alog%2810%2C5%29

log%2810%2C%28%285z%2F%28z-2%29%29%29%29=1.39794

Finding antilog of the expression in the log function,

10%5E%281.39794%29=25=%285z%29%2F%28z-2%29, although the rendering might make that hard to read.
25=5z%2F%28z-2%29
25%28z-2%29=5z
25z-50=5z
20z-50=0
20z=50
2z=5
highlight%28z=5%2F2%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Please help I am stuck on this problem.
Round to the nearest thousandth
log5(5z/z-2) = 2


log+%285%2C+%285z%2F%28z+-+2%29%29%29+=+2

5z%2F%28z+-+2%29+=+5%5E2 ------ Exponential form

5z%2F%28z+-+2%29+=+25

25%28z+-+2%29+=+5z -------- Cross-multiplying

25z - 50 = 5z

25z - 5z = 50

20z = 50

z = 50%2F20, or highlight_green%28highlight_green%282.5%29%29, or 2.500