Given log_a 2 =4, log_a 3 =5, and log_a 11 = 8, what is log_a (33)/(2a^3)?

1 Answer
Aug 12, 2018

X=(log_a 33)/(2a^3)=39/8

Explanation:

We know that ,

log_a x=y<=>

Here ,

log_a 2=4=>2=a^4 and log_a 3=5=>3=a^5

i.e. color(blue)(a^4=2 and

a^5=3=>a(color(blue)(a^4))=3=>a(color(blue)(2))=3=>color(green)(a=3/2

Now , a^4=2=>a^3color(green)((a))=2=>a^3(color(green)(3/2))=2

:.a^3=4/3=>color(red)(2a^3=8/3

Let ,

X=(log_a 33)/(2a^3)=(log_a(3xx11))/(8/3)to[:.2a^3=8/3]

:. X=(log_a3+log_a11)/(8/3)to[becauselog(m*n)=logm+logn]

:.X=(5+8)/(8/3)=(13xx3)/8=39/8