Question

If


`log_(5)(3) = a`
and

`log_(5)(4)= b`
then

`log_(15)(2)`
is?
a)2b/a+1

b)a+b/ab

c)2b-a/2b

d)b/2a+2

e)2a+2/b

​

Answer 1

`\bf \log_5(3)=a\qquad \qquad \log_5(4)=b\ \\\\\\ \log_5(4)=b\implies \log_5(2^2)=b\implies 2\log_5(2)=b\implies \log_5(2)=\cfrac{b}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_(15)(2)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_5(2)}{\log_5(15)}}\implies \cfrac{~~(b)/(2)~~}{\log_5(3\cdot 5)}\implies \cfrac{~~(b)/(2)~~}{\log_5(3)+\log_5(5)} \\\\\\ \cfrac{~~(b)/(2)~~}{a+1}\implies \cfrac{b}{2}\cdot \cfrac{1}{a+1}\implies \cfrac{b}{2a+2}`