Using log laws to manipulate and simplify

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I am reviewing this to teach this concept this year, and I have completely forgotten how to do these questions. Am I right in the fact that it needs to be some combination of multiplication, division and indices to reach 98 using 5 and 2? My instinct was 5*2*5*2-2 but that doesn't tie in with the log laws. This is frustrating me! Help!

Logs don't play well with minus signs; try factoring $98$ into primes. Remember, $\log_7 7 = 1$. — Theo Bendit, Jan 15 '19 at 04:56
ahhhh i forgot that you could use 7! need to pay more attention to the bases. Thank you so much! — Georgia F, Jan 15 '19 at 05:07

score 0 · Answer 1 · answered Jan 15 '19 at 05:27

0

$\log_7 98 = \log_7 (7^2 \times 2) = \log_7 (7^2) + \log_7 2 \approx 2.36$

$\log_7 70 = \log_7 (7 \times 5 \times 2) = \log_7 7 + \log_7 5 + \log_7 2 \approx 1 + .83 + .36 = 2.19$

answered Jan 15 '19 at 05:27

J. W. Tanner

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Using log laws to manipulate and simplify

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