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If logx2=log3 x is satisfied by two valu...

If `log_x2=log_3` x is satisfied by two values of x, what is their sum?

A

0

B

1.73

C

2.35

D

2.81

Text Solution

Verified by Experts

The correct Answer is:
D
Let y`=log_x2=log_3x`. Converting to exponential form gives `x^y=2` and `3^y=x`. Substitute to get `3^(y^2)=2`, which can be converted into `y^2=(log2)/(log3)~~0.6309`. Thus, `y~~+-0.7943`. Therefore, `3^(0.7943)=x~~2.393` or `3^(-0.7943)=x~~0.4178`. Therefore, the sum of two x's is 2.81. [8]
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