Question

If 2^x-2*3^2x-6=36, then find the value of x.

Answer 1

${2}^{x - 2} \times {3}^{2x - 6} = 36 \\ \\ {2}^{x - 2} \times {3}^{2x - 6} = 2 \times 2 \times 2 \times 3 \\ \\ {2}^{x - 2} \times {3}^{2x - 6} = {2}^{3} \times {3}^{1} \\ \\ {2}^{x - 2} = \frac{ {2}^{3} \times {3}^{1} }{ {3}^{2x - 6} } \\ \\ {2}^{x - 2} = {2}^{3} \times {3}^{1 - 2x - 6} \\ \\ {2}^{x - 2} = {2}^{3} \times {3}^{( - 2x - 5)} \\ \\ \frac{{2}^{x - 2}}{ {2}^{3} } = {3}^{( - 2x - 5)} \\ \\ {2}^{x - 2 - 3} = {3}^{( - 2x - 5)}$

Answer 2

The value of x is 4.

Step-by-step explanation:

The given equation is

$2^{x-2}\times 3^{2x-6}=36$

We have to find the value of x.

Find prime factors of 36 and rewrite the given equation.

$2^{x-2}\times 3^{2x-6}=2\times 2\times 3\times 3$

$2^{x-2}\times 3^{2x-6}=2^2\times 3^3$

On comparing the exponents of 2, we get

$x-2=2$

$x=4$

On comparing the exponents of 3, we get

$2x-6=2$

$2x=8$

$x=4$

Therefore, the value of x is 4.

#Learn more

If 2^x-2*3^2x-6=36, then find the value of x.​

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