# Exponential problem

If $$2^x = 7$$, what is $$2^{2x+5}$$?

Note by A Brilliant Member
2 years, 4 months ago

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\begin{align} 2^x=7\\&\implies 2^{2x}=7^2\\&\implies 2^{2x+5}=7^2\cdot 2^5=1568 \end{align}

- 2 years, 4 months ago

How come the $$2^x = 7$$ becomes $$2^{2x} = 7^2$$?

- 2 years, 4 months ago

Square both sides ... $(2^x)^2=7^2$

- 2 years, 4 months ago

Thanks! If the question change how to find the value of $$x$$?

- 2 years, 4 months ago

Take log :- $2^x=7\\\implies \log_2 2^x=\log_2 7\\ \implies x=\log_2 7$

- 2 years, 4 months ago

Thanks for helping me!

- 2 years, 4 months ago

Welcome $$\ddot\smile$$

- 2 years, 4 months ago