Question

If 5 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline 5, what is the value of x? â€"3 â€"2 2 3.

Answer 1

The value of x is 3.

Given that,

If  $5 + 20 \times 2^{2-3x}$,

And Baseline = $10 \times 2^{-2x}+5$

We have to find,

The value of x?

According to the question,

To determine the value of x in the equation following all the steps given below.

Equation; $\rm 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5$

• Step1; Subtract 5 from both sides,

                   $\rm5- 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5-5\\\\\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}$

• Step2; Divided by 10 on both sides,

                    $\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}\\\\\dfrac{ 20 \times 2^{2-3x} }{10}= \dfrac{10 \times 2^{-2x}}{10}\\\\\rm 2 \times 2^{2-3x} = 2^{-2x}$

• Step3; Rewrite the term into their power form and add the powers,

                   $\rm 2 \times 2^{2-3x} = 2^{-2x}\\\\2^1 \times 2^{2-3x} = 2^{-2x}\\\\2^{2-3x+1} = 2^{-2x}$

• Step4; The base is the same on both sides, we equate exponents,        

                    $\rm 2-3x+1 = -2x\\\\-3x+2x = -1-2\\\\-x = -3\\\\x=3$

Hence, The required value of x is 3.

For more details about the Exponent refer to the link given below.

brainly.com/question/25959524