Question

if 5 to the power x minus 3 into 3 to the power 2 x minus 8 is equal to 225 then find the value of x

Answer 1

5^x-3.  3^2x-8 = 225
                 = 3 × 75 
                 = 3 × 3 × 25 
                 = 3 × 3 × 5 × 5
∴ 5^x-3.  3^2x-8 = 5^2 × 3^2
Comparing both the sides we get
x − 3 = 2
⇒ x = 5  (You can compare even the other one also. The result will be same)

Answer 2

From the equation, the required value of x is 5.

Given:

The given equation is $5^{x-3}.\ 3^{2x-8}=225$

To Find:

We need to find the value of x from the given equation.

Solution:

To tackle this problem we need to have basic knowledge of exponents and powers.

$5^{x-3}.\ 3^{2x-8}=225$

write 225 in the powers of 3 and 5

$5^{x-3}.\ 3^{2x-8}=3^{2}. 5^{2}$

when bases are equal and are on either side of the equation then the powers should be equal. Consider the powers of 5.

$x-3=2$

$x=2+3$

$x=5$

Therefore, the value of x in the given equation is 5.

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