First slide

Types of real valued functions XI

Question

If $2 x^{\log_{4} 3} + 3^{\log_{4} x} = 27$ then x is equal to

Moderate

A

2
B

4
C

8
D

16

Solution

$\begin{array}{l} 2 x^{\log_{4} 3} + 3^{\log_{4} x} = 27 \\ \Rightarrow 2 \times 3^{\log_{4} x} + 3^{\log_{4} x} = 27 \\ \Rightarrow 3^{\log_{4} x} = 9 = 3^{2} \\ \Rightarrow \log_{4} x = 2 \\ ∴ x = 4^{2} = 16 . \end{array}$

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