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  4. If log 2(x3)= log 2(x2)+ log 2 5- log 2 3, then x is equal to

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Q. If $\log _2\left(x^3\right)=\log _2\left(x^2\right)+\log _2 5-\log _2 3$, then $x$ is equal to

Continuity and Differentiability

Solution:

Note that x should be positive
Now, $3 \log _2 x=2 \log _2 x+\log _2\left(\frac{5}{3}\right) \Rightarrow \log _2 x=\log _2\left(\frac{5}{3}\right) \Rightarrow x=\frac{5}{3}$