Question

# If $$2^{4} \times 4^{2} = 16^{x}$$, then find the value of x.

Solution

## $$2^{4} \times 4^{2} = 16^{x}$$ $$\Rightarrow 2^{4} \times (2^{2})^{2} = [(2)^{4}]^{x}$$ $$\Rightarrow 2^{4} \times 2^{4} = 2^{4x}$$ $$\Rightarrow 2^{4+4}= 2^{4x} \Rightarrow 2^{8} = 2^{4x}$$ Comparing, we get 4x = 8 $$\Rightarrow$$ x = $$\frac{8}{4}$$ = 2 $$\therefore$$ x = 2 MathematicsRD SharmaStandard IX

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