Find - x - if 8x-2-1-24-3 x-0-0625x-

The correct option is D 1The given expression is: 8^x 2× ( 1/2 )^(4 3x)=(0.0625)^x ⇒ 2^3(x 2)× (1/2 )^(4 3x)= ( 1/16 )^x ⇒2^(3x 6)/2^(4 3x)= ( 1/2 )^4x ⇒ 2^(3x ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

Find ' x ', i...

Question

Find 'x', if $8^{x - 2} \times {(\frac{1}{2})}^{4 - 3 x} = (0.0625)^{x} .$

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Solution

The correct option is D 1
The given expression is:
$8^{x - 2} \times {(\frac{1}{2})}^{(4 - 3 x)} = (0.0625)^{x} \Rightarrow 2^{3 (x - 2)} \times {(\frac{1}{2})}^{(4 - 3 x)} = {(\frac{1}{16})}^{x} \Rightarrow \frac{2^{(3 x - 6)}}{2^{(4 - 3 x)}} = {(\frac{1}{2})}^{4 x} \Rightarrow 2^{(3 x - 6 - (4 - 3 x))} = 2^{(- 4 x)} \Rightarrow 2^{(6 x - 10)} = 2^{(- 4 x)} \Rightarrow 6 x - 10 = - 4 x (multiplying both sides by log base 2) \Rightarrow 10 x = 10 \Rightarrow x = 1.$

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Find 'x', if 8x−2×(12)4−3x=(0.0625)x.

The correct option is D 1The given expression is: 8x−2×(12)(4−3x)=(0.0625)x⇒23(x−2)×(12)(4−3x)=(116)x⇒2(3x−6)2(4−3x)=(12)4x⇒2(3x−6−(4−3x))=2(−4x)⇒2(6x−10)=2(−4x)⇒6x−10=−4x(multiplying both sides by log base 2)⇒10x=10⇒x=1.

Find 'x', if $8^{x - 2} \times {(\frac{1}{2})}^{4 - 3 x} = (0.0625)^{x} .$