Question

2^2x * 2^x+9 = (4^3)^6
${2}^{2x} \times {2}^{x + 9 } = {( {4}^{3} )}^{6}$
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Answer 1

Answer:

x = 3

2^2x * 2^x * 2^9= 4^18

4^3x+9= 4^18

3x+9 = 18

x = 3

Answer 2

$\huge\mathfrak{Question}$

${2}^{2x} \times {2}^{x + 9 } = {( {4}^{3} )}^{6}$

$\large\tt{Solution}$

$2 ^{2x} \times {2}^{x + 9} =(( {2}^{2} )^{3} \: )^{6}$

${2}^{2x} \times {2}^{x + 9 } = ( {2}^{6} )^{6}$

${2}^{2x} \times {2}^{x + 9 } = {2}^{36}$

✔As the bases are same we can evalute the powers

$2x \times x + 9 = 36$

$2 {x}^{2} + 9 = 36$

${2x}^{2} = 36 - 9$

${2x}^{2} = 27$

${x}^{2} = \frac{27}{2}$

$x = \sqrt{ \frac{27}{2} }$

$x = 3.67(approx.)$