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If 2x^{{log_4}^3}+3^{_4x}=27, then x is equal to?

Question

If $2 x^{l o g_{4}^{3}} + 3^{l o g_{4} x} = 27$ , then x is equal to?

2

4

8

16

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Scarlett Discussed

2 x^{l o g_{4}^{3}} + 3^{l o g_{4} x} = 27

, then x is equal to?

14 mins ago

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14 mins ago

Text solutionVerified

2 \times x^{l o g_{4} 3} + 3^{l o g_{4} x} = 27

2 \times 3^{l o g_{4} x} + 3^{l o g_{4} x} = 27

Let

3^{l o g_{4} x} = t

2 t + t = 27

3 t = 27

t = 9

3^{l o g_{4}^{x}} = 3^{2} = 9

So,

l o g_{4} x = 2

So,

x = 2^{4} = 16

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