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If \(2^x = 7\), what is \(2^{2x+5}\)?

Note by Cedie Camomot 1 year, 6 months ago

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\[\begin{align} 2^x=7\\&\implies 2^{2x}=7^2\\&\implies 2^{2x+5}=7^2\cdot 2^5=1568 \end{align}\] – Rishabh Cool · 1 year, 6 months ago

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@Rishabh Cool – How come the \(2^x = 7 \) becomes \(2^{2x} = 7^2\)? – Cedie Camomot · 1 year, 6 months ago

@Cedie Camomot – Square both sides ... \[(2^x)^2=7^2\] – Rishabh Cool · 1 year, 6 months ago

@Rishabh Cool – Thanks! If the question change how to find the value of \(x\)? – Cedie Camomot · 1 year, 6 months ago

@Cedie Camomot – Take log :- \[2^x=7\\\implies \log_2 2^x=\log_2 7\\ \implies x=\log_2 7\] – Rishabh Cool · 1 year, 6 months ago

@Rishabh Cool – Thanks for helping me! – Cedie Camomot · 1 year, 6 months ago

@Cedie Camomot – Welcome \(\ddot\smile\) – Rishabh Cool · 1 year, 6 months ago

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## Comments

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TopNewest\[\begin{align} 2^x=7\\&\implies 2^{2x}=7^2\\&\implies 2^{2x+5}=7^2\cdot 2^5=1568 \end{align}\] – Rishabh Cool · 1 year, 6 months ago

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– Cedie Camomot · 1 year, 6 months ago

How come the \(2^x = 7 \) becomes \(2^{2x} = 7^2\)?Log in to reply

– Rishabh Cool · 1 year, 6 months ago

Square both sides ... \[(2^x)^2=7^2\]Log in to reply

– Cedie Camomot · 1 year, 6 months ago

Thanks! If the question change how to find the value of \(x\)?Log in to reply

– Rishabh Cool · 1 year, 6 months ago

Take log :- \[2^x=7\\\implies \log_2 2^x=\log_2 7\\ \implies x=\log_2 7\]Log in to reply

– Cedie Camomot · 1 year, 6 months ago

Thanks for helping me!Log in to reply

– Rishabh Cool · 1 year, 6 months ago

Welcome \(\ddot\smile\)Log in to reply