Question

Determine (8x)x , if $\9^{x+2}$ = 240+9x.

Answer 1

$\large\bold\pink{\: \: \: Topic:~ Laws~ of~ exponents}$

Given:

• $\sf{9^{x+2} = 240 + 9^{x}}$

To Find:

• Value of x ?

Solution:

$\large\implies\sf{\: \: \: \: 9^{x} \times 9^{2} - 9^{x} = 240}$

$\large\implies\sf{\: \: \: \: 9^{x} (81-1) = 240}$

$\large\implies\sf{\: \: \: \: 80 \times 9^{x} = 240 }$

$\large\implies\sf{\: \: \: \: 9^{x} = \frac{240}{80} = 3}$

$\large\implies\sf{\: \: \: \: 3^{2^{x}} = 3}$

$\large\implies\sf{\: \: \: \: 2x = 1 }$

$\large\implies\sf{\: \: \: \: x = \frac{1}{2} }$

$\large\therefore\sf{\: \: \: \: (8x)^{x} = (8 \times \frac{1}{2})^{\frac{1}{2}} = 4^{\frac{1}{2}} = (2^{2}^{\frac{1}{2}} = 2^{2 \times \frac{1}{2}} = 2^{1} = 2}$

$\large{\underline{\pmb{\mathsf{Hence,~ Value~ of~ x~ is~ 2.}}}}$

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