Question

5^n-2×3^2n-3=135 find n?

Answer 1

factrize135 and after it compare powers

Answer 2

Concept Introduction:

Exponents rule to be applied is $a^{n}$ ·$a^{m}$ = $a^{m+n}$  .

Given: It is given that $5^{n-2}$ × $3^{2n-3}$ = $135$.

To Find:

We have to find the value of, n from the given equation.

Solution:

According to the problem,

 $5^{n-2}$ × $3^{2n-3}$ = $135$

⇒$\frac{5^{n} }{5^{2} }$ × $\frac{3^{2n} }{3^{3} }$ = $135$

⇒$5^{n}$ × $3^{2n}$ = $135$ × $25$ × $27$

⇒$5^{n}$ × $9^{n}$ = $5^{3}$ × $9^{3}$

∴ n = $3$

Final Answer:

The value of n is $3$.

#SPJ3