Question

solve the following exponential equations: 4^x ×2^x=(32)1/5 ×(8)1/3

Answer 1

Answer :

Given that,

${4}^{x} \times {2}^{x} = {32}^{ \frac{1}{5} } \times {8}^{ \frac{1}{3} } \\ \\ \implies {( {2}^{2} )}^{x} \times {2}^{x} = {( {2}^{5} )}^{ \frac{1}{5} } \times { ({2}^{3}) }^{ \frac{1}{3} } \\ \\ \implies {2}^{2x} \times {2}^{x} = {2}^{ \frac{5}{5} } \times {2}^{ \frac{3}{3} } \\ \\ \implies {2}^{(2x + x)} = {2}^{1} \times {2}^{1} \\ \\ \implies {2}^{3x} = {2}^{(1 + 1)} \\ \\ \implies {2}^{3x} = {2}^{2}$

Now, comparing the like powers of 2, we get

3x = 2

i.e., x = $\frac{2}{3}$

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