New user? Sign up

Existing user? Sign in

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

Note by Cedie Camomot 1 year, 10 months ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

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

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

Sort by:

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

Log in to reply

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 \(x\)?

@Cedie Camomot – Take log :- \[2^x=7\\\implies \log_2 2^x=\log_2 7\\ \implies x=\log_2 7\]

@Rishabh Cool – Thanks for helping me!

@Cedie Camomot – Welcome \(\ddot\smile\)

Problem Loading...

Note Loading...

Set Loading...

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

Sort by:

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

Log in to reply

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

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply