An algebra problem by prasanth pp

Algebra Level 2

If $m = \log_7 2$ , find the value of $\log_{49} 28$ in terms of $m$ .

1+m

\frac{1+2m}{2}

\frac{2}{1+2m}

2(1+2m)

\frac{1}{1+2m}

1 solution

Prasanth Pp
Apr 10, 2016

Given $log_{7}2=m....................(1)$

$log_{49}28= \frac{log_{7}28}{log_{7}49}$ (Note:base changing rule)

$= \frac{log_{7}(2^{2} \times 7 )}{log_{7}7^{2}}$
$= \frac{(log_{7}7)+(log_{7}(2^{2} )}{2}$
$= \frac{1+2(log_{7}2) }{2}$
$= \frac{1+2m}{2}$ (from...(1))

An algebra problem by prasanth pp

1 solution

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