SOLUTION: Given log 16=1.2, log 5=0.7 and log 8=0.9 Find log1/49

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Question 1049679: Given log 16=1.2, log 5=0.7 and log 8=0.9 Find log1/49
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
log1/49 ?
log%28%281%2F49%29%29
log%28%281%2F7%5E2%29%29
log%28%287%5E%28-2%29%29%29
-2%2Alog%28%287%29%29-----------You want to know log of 7. It would be somewhere between log of 5 and log of 8. You might like to try linear interpolation. 

    input      |     log of input
               |
               |
----------------------------------------
    5          |          0.7
    7          |         log((7))=y
    8          |          0.9
----------------------------------------


y=mx+b
y=%28%280.9-0.7%29%2F%288-5%29%29x%2Bb
y=%280.2%2F3%29x%2Bb
y=%282%2F30%29x%2Bb
y=x%2F15%2Bb
-
Pick either of the two points.
b=y-x%2F15
b=0.9-8%2F15=9%2F10-8%2F15
b=27%2F30-16%2F30
b=11%2F30
highlight%28log%28%28x%29%29=x%2F15%2B11%2F30%29----------important but not your final answer of log%28%281%2F49%29%29.


FINISHING
Input was 7.
log%28%281%2F49%29%29
log%28%287%5E%28-2%29%29%29
-2%2Alog%28%287%29%29
-2%287%2F15%2B11%2F30%29
-2%2818%2F30%29
-2%283%2A6%29%2F%286%2A5%29
-2%283%2F5%29
highlight%28-6%2F5%29 or highlight%28-1%261%2F5%29