# Using log laws to manipulate and simplify

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!

• For i) Think: $7$ to the what power equals $98$? – MathIsLife12 Jan 15 at 4:56
• Logs don't play well with minus signs; try factoring $98$ into primes. Remember, $\log_7 7 = 1$. – Theo Bendit Jan 15 at 4:56
• ahhhh i forgot that you could use 7! need to pay more attention to the bases. Thank you so much! – Georgia F Jan 15 at 5:07

$$\log_7 98 = \log_7 (7^2 \times 2) = \log_7 (7^2) + \log_7 2 \approx 2.36$$
$$\log_7 70 = \log_7 (7 \times 5 \times 2) = \log_7 7 + \log_7 5 + \log_7 2 \approx 1 + .83 + .36 = 2.19$$