Solve for $x$ if $2^{x+1}+2^{x+2}=192$.

Given:

$2^{x+1}+2^{x+2}=192$

To do:

We have to find the value of $x$.

Solution:
$2^{x+1}+2^{x+2}=192$

$2\times2^x+2^2\times2^x=192$

$(2+4)\times2^x=192$

$2^x=\frac{192}{6}$

$2^x=32$

$2^x=2^5$

Comparing powers on both sides, we get,

$x=5$
The value of $x$ is $5$. 

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Updated on: 10-Oct-2022

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