Question

find the value of x if 125/27 multiplied by (125/27) power x =(5/3) power 18​

Answer 1

solution:

( 125/5 *125/5 )^x = (5/3)^18

(15625/25)^x = (5/3)^18

(625)^x =( 5/3)^18

((5)^3)^x=(5/3)^18

(5)^x =(5/3)^18/3

(5)^x=(5/3)^6

(5)^x=(25/9)^3

Answer 2

Given:

An exponential equation$(\frac{125}{27})^{x} = (\frac{5}{3})^{18}$.

To Find:

The value of x is?

Solution:

1. The formula used to solve the given problem is,

• $a^{{m^n}}$=$a^{mn}$

2. The given equation is,

=>  $(\frac{125}{27})^{x} = (\frac{5}{3})^{18}$

It can be also written as,

=> $(\frac{5^3}{3^3})^{x} = (\frac{5}{3})^{18}$

=> $(\frac{5}{3})^{3x} = (\frac{5}{3})^{18}$ ( From the mentioned formula )

3. The powers can now be equated as the base values are equal,

=> $(\frac{5}{3})^{3x} = (\frac{5}{3})^{18}$

=> 3x = 18,

=> x = 18/3,

=> x = 6.

Therefore, the value of x is 6.