Question

find the value of m if 9x3^m=27^2m-3​

Answer 1

➤ Given:

The equation:-

$\bf 9 \times 3^m = 27^{2m-3}$

➤ What To Find:

We have to find the value of m.

➤ How To Find:

• First, we have to simplify the equation to make the same base on both sides.
• Next, excluding the bases, directly solve the equation.

➤ Solution:

• Make the bases the same.

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

Here 9 can be written as 3²,

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

Here 27 can be written as 3³,

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

• Solve the exponents.

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

Remove the bases,

$\sf \implies 2 + m = 3(2m-3)$

Remove the brackets in RHS,

$\sf \implies 2 + m = 6m-9$

Take m to RHS,

$\sf \implies 2 = 6m - 9 - m$

Take -9 to LHS,

$\sf \implies 2 + 9= 6m - m$

Solve the LHS,

$\sf \implies 11 = 6m - m$

Solve the RHS,

$\sf \implies 11 = 5m$

Take 5 to LHS,

$\sf \implies \dfrac{11}{5} = m$

Divide 11 by 5,

$\sf \implies 2.2 = m$

$\underbrace{\overline{\boxed{ \rm \therefore The \: value \: of \: m \: is \: 2.2 .}}}$

Answer 2

➤ Given:

The equation:-

$\bf 9 \times 3^m = 27^{2m-3}$

➤ What To Find:

We have to find the value of m.

➤ How To Find:

First, we have to simplify the equation to make the same base on both sides.

Next, excluding the bases, directly solve the equation.

➤ Solution:

Make the bases the same.

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

Here 9 can be written as 3²,

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

Here 27 can be written as 3³,

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

Solve the exponents.

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

Remove the bases,

$\sf \implies 2 + m = 3(2m-3)$

Remove the brackets in RHS,

$\sf \implies 2 + m = 6m-9$

Take m to RHS,

$\sf \implies 2 = 6m - 9 - m$

Take -9 to LHS,

$\sf \implies 2 + 9= 6m - m$

Solve the LHS,

$\sf \implies 11 = 6m - m$

Solve the RHS,

$\sf \implies 11 = 5m$

Take 5 to LHS,

$\sf \implies \dfrac{11}{5} = m$

Divide 11 by 5,

$\sf \implies 2.2 = m$

$\underbrace{\overline{\boxed{ \rm \therefore The \: value \: of \: m \: is \: 2.2 .}}}$