SOLUTION: Use log5(2)~.4307 and log5(3)~.6826 to approximate the expression without a calculator: log5(18)

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Question 72883: Use log5(2)~.4307 and log5(3)~.6826 to approximate the expression without a calculator:
log5(18)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use these identities to solve
ylog%28x%29=log%28x%29%5Ey
log%28x%29%2Blog%28y%29=log%28x%2Ay%29
If we let x=2 and y=3 for the 1st identity we get
2%2Alog_%5B5%5D%283%29=log_%5B5%5D%283%5E2%29=log_%5B5%5D%289%29This gets us halfway to 18.
2%2Alog_%5B5%5D%283%29=2%2A%280.6826%29=1.3652Now plug in the approximate values
log_%5B5%5D%282%29%2Blog_%5B5%5D%289%29=log_%5B5%5D%282%2A9%29=log_%5B5%5D%2818%29Notice how this turns into log(18) using the identities.
0.4307%2B1.3652=1.7959Plug in remaining values.
Check:
5%5E1.7959=18.00032It's close enough to work
So log_%5B5%5D%2818%29=1.7959Approximately of course