SOLUTION: Use the change of base formula to express log4 of 67 in terms of common logarithms and then approximate it to the nearest thousandth? I'm having trouble working this problem out, i

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Question 826045: Use the change of base formula to express log4 of 67 in terms of common logarithms and then approximate it to the nearest thousandth? I'm having trouble working this problem out, if you could help me that would be appreciated! thank you:)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Change of Base Formula, log%28b%2Ca%29=%28log%2810%2Ca%29%29%2F%28log%2810%2Cb%29%29 if converting to base ten.

log%284%2C67%29=log%2810%2C67%29%2Flog%2810%2C4%29
log%2810%2C%286.7%2A10%5E1%29%29%2Flog%2810%2C4%29
%28log%2810%2C6.7%29%2Blog%2810%2C10%5E1%29%29%2F%28log%2810%2C4%29%29
Use Table of Logarithms
%280.8261%2B1%29%2F0.602
1.8261%2F0.602
highlight%283.03%29

Approximate Check: 4%5E3=64;
the exponent would be slightly higher than 3 to reach 67.