SOLUTION: log base 4 of y + log base2 of y =12 solve for y

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Question 1205633: log base 4 of y + log base2 of y =12
solve for y

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.
log base 4 of y + log base2 of y =12
solve for y
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Your starting equation is

    log%284%2C%28y%29%29 + log%282%2C%28y%29%29 = 12.    (1)


Use the base change formula

    log%282%2C%28y%29%29 = log%284%2C%28y%29%29%2Flog%284%2C%282%29%29 = log%284%2C%28y%29%29%2F%28%281%2F2%29%29 = 2%2Alog%284%2C%28y%29%29.


Therefore, equation (1) takes the form

    log%284%2C%28y%29%29 + 2%2Alog%284%2C%28y%29%29 = 12

    3%2Alog%284%2C%28y%29%29 = 12

    log%284%2C%28y%29%29 = 12/3 = 4

    y = 4%5E4 = 256.


ANSWER.  y = 256.

Solved.

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On logarithms and their properties,  see these introductory lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Evaluate logarithms without using a calculator
    - Simplifying expressions with logarithms
    - Solving logarithmic equations
in this site.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log+%284+%2Cy+%29%2B+log+%282+%2Cy%29+=12.......change to base 10

log+%28y+%29%2Flog+%284%29%2B+log+%28y%29+%2Flog+%282+%29=12

%28log+%28y+%29log+%282%29%2B+log+%28y%29log+%284%29%29+%2F%28log+%284%29log+%282+%29%29=12

log+%28y+%29log+%282%29%2B+log+%28y%29log+%284%29+=12%28log+%284%29log+%282+%29%29

log+%28y+%29%28log+%282%29%2B+log+%284%29+%29=12%28log+%284%29log+%282+%29%29

log+%28y+%29%28log+%282%2A4%29+%29=12%28log+%284%29log+%282+%29%29

log+%28y+%29%2Alog+%282%5E3%29+=12%28log+%284%29log+%282+%29%29

log+%28y+%29%2A3log+%282%29+=12%28log+%284%29log+%282+%29%29

log+%28y+%29=%2812%28log+%284%29log+%282+%29%29%29%2F%283log+%282%29+%29....simplify



log+%28y+%29=4%2Alog+%284%29

log+%28y+%29=log+%284%5E4%29

y=4%5E4

y=256