Question

If 2^x-2^x-1=16,then find the value of x^2 is

Answer 1

Answer:

x² = 25

Step-by-step explanation:

This is the answer with explanation

Answer 2

Answer:

Concept:

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion. To illustrate 3 x 3 x 3 x 3 in a straightforward manner, for instance, we could write it as 34, where 4 is the exponent and 3 is the base. It is claimed that the entire statement 34 has power.

Power is just an expression that displays the same number or factor being multiplied again. The number of times the base is multiplied by itself determines the exponent's value.

Step-by-step explanation:

Given:

$2^{x}-2^{x-1}=16$

Find:

Find the value of  $x^{2}$

Solution:

Given equation

                       =  $2^{x}-2^{x-1}=16$

Now write the number 16 in power form

                        =  $2^{x}-2^{x-1}=2^{4}$

Now simplify the x-1 term by sending "-1" to right-hand side of the equation,

                        $\Rightarrow$ $2^{x}-2^{x}=2^{4+1}$

                        $\Rightarrow$   $2^{x}-2^{x}=2^{5}$

Hence comparing the x value from the obtained equation,

                                  x = 5

Now we want to find the value of $x^{2}$

By substituting the value of 'x'  = $(5)^{2}$ = 25

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