Question

5^x-2×3^2x-3=135 find x?

Answer 1

5^x-2*3^2x-3=135
-2-3=135-5^x/3^2x
-5=135-5/9
-5=15-5
-5=10
x=10+5
x=15

Answer 2

Answer:

The value of x here is 3.

To find:

The value of x.

Solution:

Given

$5 ^ { x - 2 } \times 3 ^ { 2 x - 3 } = 135$

Factorizing, 135, we get,

$\begin{array} { c } { \therefore 135 = 5 \times 3 \times 3 \times 3 \times 1 = 5 \times 3 ^ { 3 } } \\\\ { 5 ^ { x - 2 } \times 3 ^ { 2 x - 3 } = 135 } \\\\ { 5 ^ { x - 2 } \times 3 ^ { 2 x - 3 } = 5 \times 3 ^ { 3 } \ldots \ldots \text { (i) } } \end{array}$

From (i)

Either

$\begin{array} { c } { 5 ^ { x - 2 } = 5 ^ { 1 } } \\\\ { x - 2 = 1 } \\\\ { x = 1 + 2 } \\\\ { \quad x = 3 } \end{array}$

Or

$\begin{array} { c } { 3 ^ { 2 x - 3 } = 3 ^ { 3 } } \\\\ { 2 x - 3 = 3 } \\\\ { 2 x = 3 + 3 = 6 } \\\\ { x = \frac { 6 } { 2 } = 3 } \\\\ { \therefore x = 3 } \end{array}$

Hence, the value of x is 3.