SOLUTION: Given that loga2=0.3010 and loga3=0.4771, find loga18

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Question 144254: Given that loga2=0.3010 and loga3=0.4771, find loga18
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28a%2C%283%29%29=0.4771 Start with the second equation


2%2Alog%28a%2C%283%29%29=2%2A0.4771 Multiply both sides by 2


2%2Alog%28a%2C%283%29%29=0.9542 Multiply 2 and 0.4771 to get 0.9542


log%28a%2C%283%5E2%29%29=0.9542 Rewrite the expression using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%28a%2C%289%29%29=0.9542 Square 3 to get 9


log%28a%2C%289%29%29%2Blog%28a%2C%282%29%29 Now add log%28a%2C%282%29%29


log%28a%2C%289%2A2%29%29 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


log%28a%2C%2818%29%29 Multiply


Since log%28a%2C%2818%29%29=log%28a%2C%289%29%29%2Blog%28a%2C%282%29%29 , this means that log%28a%2C%2818%29%29=0.9542%2B0.3010=1.2552



So log%28a%2C%2818%29%29=1.2552