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Exponential problem

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

Note by Cedie Camomot
6 months, 3 weeks 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 · 6 months, 3 weeks ago

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@Rishabh Cool How come the \(2^x = 7 \) becomes \(2^{2x} = 7^2\)? Cedie Camomot · 6 months, 3 weeks ago

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@Cedie Camomot Square both sides ... \[(2^x)^2=7^2\] Rishabh Cool · 6 months, 3 weeks ago

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@Rishabh Cool Thanks! If the question change how to find the value of \(x\)? Cedie Camomot · 6 months, 3 weeks ago

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@Cedie Camomot Take log :- \[2^x=7\\\implies \log_2 2^x=\log_2 7\\ \implies x=\log_2 7\] Rishabh Cool · 6 months, 3 weeks ago

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@Rishabh Cool Thanks for helping me! Cedie Camomot · 6 months, 3 weeks ago

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@Cedie Camomot Welcome \(\ddot\smile\) Rishabh Cool · 6 months, 3 weeks ago

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