SOLUTION: solve for x:(1/4)^x=14

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Question 997659: solve for x:(1/4)^x=14
Found 4 solutions by MathLover1, josgarithmetic, rothauserc, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
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%281%2F4%29%5Ex=14........use log
log%28%281%2F4%29%5Ex%29=log%2814%29
x%2Alog%28%281%2F4%29%29=log%282%2A7%29
x%2A%28log%28%281%29-log%284%29%29%29=log%282%29%2Blog%287%29
x%2A%280-log%284%29%29=log%282%29%2Blog%287%29
x=%28log%282%29%2Blog%287%29%29%2F%28-2log%282%29%29
x=-%28log%282%29%2Blog%287%29%29%2F%282log%282%29%29
x+=+-1.90

Answer by josgarithmetic(39616) About Me  (Show Source):
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ln%28%281%2F4%29%5Ex%29=ln%2814%29
x%2Aln%281%2F4%29=ln%2814%29
x=ln%2814%29%2Fln%281%2F4%29
highlight%28x=-ln%2814%29%2Fln%284%29%29-----use calculator or a table of natural logarithms.

Answer by rothauserc(4718) About Me  (Show Source):
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(1/4)^x = 14
use definition of logarithm
log(base 1/4) of 14 = x
x is approx -1.90

Answer by MathTherapy(10551) About Me  (Show Source):
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solve for x:(1/4)^x=14
Easiest method: %281%2F4%29%5Ex+=+14 

4%5E%28-+x%29+=+14 ------> %281%2F4%29%5Ex is equivalent to 4%5E%28-+x%29

log+%284%2C+14%29+=+-+x ------- Converting to logarithmic form

log%2814%29%2Flog%284%29+=+-+x ------ Applying change of base

1.903677461 = - x

x = 1.903677461%2F%28-+1%29 -------> highlight_green%28x+=+-+1.903677461%29