First slide

Types of real valued functions XI

Question

If $(4)^{\log_{9} 3} + (9)^{\log_{2} 4} = (10)^{\log_{x} 83}$ then x is equal to

Moderate

A

2
B

3
C

10
D

30

Solution

$\begin{array}{l} {(4)}^{\log_{9} 3} + (9)^{\log_{2} 4} = (10)^{\log_{x} 83} \\ or (4)^{\frac{1}{2} \log_{3} 3} + (9)^{2 \log_{2} 2} = (10)^{\log_{x} 83} \\ or 2 + 81 = (10)^{\log_{x} 83} \\ or 83 = (10)^{\log_{x} 83} \\ \Rightarrow x = 10 \end{array}$

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