Question

solve the following exponential equations 2^x=(root2)^4 × (128)^1/7

Answer 1

Answer :

Given that,

${2}^{x} = {( \sqrt{2} )}^{4} \times {128}^{ \frac{1}{7} } \\ \\ \implies {2}^{x} = {( {2}^{ \frac{1}{2} }) }^{4} \times {( {2}^{7}) }^{ \frac{1}{7} } \\ \\ \implies {2}^{x} = {2}^{ \frac{4}{2} } \times {2}^{ \frac{7}{7} } \\ \\ \implies {2}^{x} = {2}^{2} \times {2}^{1} \\ \\ \implies {2}^{x} = {2}^{(2 + 1)} \\ \\ \implies {2}^{x} = {2}^{3}$

Now, comparing the like powers of 2 from both sides, we get

x = 3

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