Question

2 raise to the power of X + 1 is equals to 64

Answer 1

Hey there !

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$2 {}^{x + 1} = 64 \\ \\ 2 {}^{x + 1} = 2 {}^{6}$

Both have same base , i.e., 2.

Hence, on cancelling 2 both sides , we have ;

$2 {}^{x + 1} = 2 {}^{6} \\ \\ \cancel{ 2} \: {}^{x + 1} = \cancel{ 2} \: {}^{6} \\ \\ x + 1 = 6 \\ \\ x = 6 - 1 \\ \\ x = 5$

Hence, the value of x is found.

Now, Verification:

On substituting the value of x.

$2 {}^{x + 1} = 64 \\ \\ 2 {}^{5 + 1} = 64 \\ \\ 2 {}^{6} = 64 \\ \\ 64 = 64$

Hence, LHS = RHS.

Therefore, value of x is 5.

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Thanks for the question!

Answer 2

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Question:-


$\bold{ {2}^{x + 1} = 64}$

$\bold{ {2}^{x + 1} = {2}^{6}}$

Here,

*Cancelled 2 on both sides of terms;

$\bold{x + 1 = 6}$
$\bold{x = 6 - 1 = 5}$

$\bold{x = 5}$

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Verify:-

$\bold{ {2}^{x + 1} = 64}$

Substitute the value of x

$\bold{ {2}^{5 + 1} = 64}$
$\bold{ {2}^{6} = 64}$
$\bold{64 = 64}$

Hence,LHS=RHS

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