SOLUTION: Given that log 27+log base b 4=5 and log base a 27-log base a 4=1 without using tables find the values of a and b

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Question 1208680: Given that log 27+log base b 4=5 and log base a 27-log base a 4=1 without using tables find the values of a and b

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


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Given that log red%28base%29 red%28a%29 27+log base b 4=5 and log base a 27-log base red%28cross%28a%29%29 red%28b%29 4=1

log%28a%2C27%29%2Blog%28b%2C4%29=5
log%28a%2C27%29-log%28b%2C4%29=1

Add the two equations:

2log%28a%2C27%29=6
log%28a%2C27%29=3
a%5E3=27
a=3

Substitute a=3 in either original equation:

log%283%2C27%29%2Blog%28b%2C4%29=5
3%2Blog%28b%2C4%29=5
log%28b%2C4%29=2
b%5E2=4
b=2

ANSWERS: a=3, b=2