Question

Find M, if 9×3^m = (27)^2m-3​

Answer 1

Given:

The equation:-

$\sf (9 \times 3 )^m = (27)^{2m - 3}$

What To Find:

We have to find the value of m.

How To Find:

To find m we have to,

• Make the same base on both sides.
• Form a linear equation for the exponents.

Solution:

• Making the same bases.

$\sf (9 \times 3 )^m = (27)^{2m - 3}$

Multiply 9 by 3 in LHS,

$\sf \Rightarrow (27 )^m = (27)^{2m - 3}$

Remove the brackets,

$\sf \Rightarrow 27^m = 27^{2m - 3}$

∴ Now, the bases are the same.

• Forming the equation.

$\sf \Rightarrow 27^m = 27^{2m - 3}$

Since the bases are the same,

$\sf \Rightarrow m = 2m - 3$

Take m to RHS,

$\sf \Rightarrow 2m - 3 - m$

Take -3 to LHS,

$\sf \Rightarrow 3 = 2m - m$

Subtract m from 2m,

$\sf \Rightarrow 3 = m$

∴ Hence, the value of m in the given equation is 3.