Question

If $lo{g}_{7}2=m,thenlo{g}_{49}28$ is equal to

• A. $2(1+2m)$
• B. $\frac{1+2m}{2}$
• C. $\frac{2}{1+2m}$
• D. $1+m$

Answer 1

The correct option is B $\frac{1+2m}{2}$

$lo{g}_{49}28=\frac{log28}{log49}=\frac{log7+log4}{2log7}$
$=\frac{log7}{2log7}+\frac{log4}{2log7}=\frac{1}{2}+\frac{1}{2}lo{g}_{7}4$
$=\frac{1}{2}+\frac{1}{2}.2lo{g}_{7}2=\frac{1}{2}+lo{g}_{7}2=\frac{1}{2}+m=\frac{1+2m}{2}$