First slide

Trigonometric Identities

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

$\log_{9} (3) = \log_{9} {(9)}^{\frac{1}{2}} = 1 / 2$ ,
$\log_{2} (4) = \log_{2} {(2)}^{2} = 2$
$4^{\frac{1}{2}} + 9^{2} = 10^{\log_{x} (83)} 83 = 10^{\log_{x} (83)} \Rightarrow x = 10$

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