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

Note by A Brilliant Member 2 years, 4 months ago

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

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How come the \(2^x = 7 \) becomes \(2^{2x} = 7^2\)?

Square both sides ... \[(2^x)^2=7^2\]

@Rishabh Cool – Thanks! If the question change how to find the value of \(x\)?

@A Brilliant Member – Take log :- \[2^x=7\\\implies \log_2 2^x=\log_2 7\\ \implies x=\log_2 7\]

@Rishabh Cool – Thanks for helping me!

@A Brilliant Member – Welcome \(\ddot\smile\)

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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

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How come the \(2^x = 7 \) becomes \(2^{2x} = 7^2\)?

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Square both sides ... \[(2^x)^2=7^2\]

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