Question

what is the value of x/y if (3)x=1/16 & (3)y =32​

Answer 1

log2^4 base 3=x

log2^5 base 3=y

log2^4/log2^5=x/y

4/5×1=x/y

Answer 2

Answer:

$\frac{-4}{5} = \frac{x}{y}$

Step-by-step explanation:

Given :

$3^x = \frac{1}{16}$,

$3^y = 32$,

Then, ind the value of $\frac{x}{y}$,.

Solution :

$3^x = \frac{1}{16} = 2^{-4}$

⇒ $log_32^{-4} = x$

⇒ $-4log_32 = x$ ...(i)

$3^y = 32 = 2^{5}$

⇒ $log_32^{5} = y$

⇒ $5log_32 = y$ ...(ii)

By dividing both the equtions,

We get,

⇒ $\frac{-4log_32}{5log_32} = \frac{x}{y}$

⇒ $\frac{-4}{5} = \frac{x}{y}$