Question

Indices and Logarithms
@rational

Answer 1

Given that \[\log_m5=0.5~andlog_m7=0.8,find~the~value~of\]
\[a)\log_m9.8\]

Answer 2

gimmick is to write \(9.8\) in terms of \(5\) and\(7\) only

Answer 3

\[9.8=\frac{98}{10}=\frac{49}{5} = \frac{7^2}{5}\]

Answer 4

that'll do it

Answer 5

\[=\log_m7^2\div~\log_m5\]

Answer 6

\[=2(0.8)-0.5\]

Answer 7

careful,
\[\log \left(\frac{a}{b}\right) \ne \frac{\log (a)}{\log (b)}\]

Answer 8

that's for sure !

Answer 9

\[=1.6-0.5\]\[=1.1\] Thnx @rational @satellite73 :)

Answer 10

yw