Mathematics: Solve exponential equation: 2^x * 2^x-2= √2 (picture included)

Solve exponential equation: 2^x * 2^x-2= √2 (picture

Ответ:

lopezma152

13.03.2022

ANSWER

x = 5/4

EXPLANATION

$2^x \cdot 2^{x-2} = \sqrt{2}$

Note that $\sqrt{a} = a^{\frac{1}{2}}$ so $\sqrt{2} = 2^{\frac{1}{2} }$
Note that on the left-hand side, we can use exponent properties for multiplying two powers of the same base together: $a^x \cdot a^y = a^{x+y}$

$\begin{aligned}
2^x \cdot 2^{x-2} &= \sqrt{2} \\
2^{x + (x-2)} &= 2^{\frac{1}{2}} \\
2^{2x - 2} &= 2^{\frac{1}{2}}
\end{aligned}$

We can now equate the exponents because both sides of the equation are of the same base with no other terms.

$\begin{aligned}
2^{2x - 2} &= 2^{\frac{1}{2}} \\
2x - 2 &= \tfrac{1}{2} \\
2x &= \tfrac{1}{2} + 2 \\ 
2x &= \tfrac{5}{2} \\
x &= \tfrac{5}{4}
\end{aligned}$

The answer is x = 5/4. We can confirm this by using this value in the original equation to get a true statement.

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Ответ:

abbybarrera6187

13.03.2022

Mathematics

Hi there!

Th' Eqⁿ is :-

$2^x × 2^{x-2} = \sqrt{2}$

$\begin{aligned}
2^x \cdot 2^{x-2} &= \sqrt{2} \\
2^{x + (x-2)} &= 2^{\frac{1}{2}} \\
2^{2x - 2} &= 2^{\frac{1}{2}}
\end{aligned}$

Equating the Exponent :-

Cuz' both sides of the equation have th' same base with no other terms.

$\begin{aligned}
2^{2x - 2} &= 2^{\frac{1}{2}} \\
2x - 2 &= \tfrac{1}{2} \\
2x &= \tfrac{1}{2} + 2 \\ 
2x &= \tfrac{5}{2} \\
x &= \tfrac{5}{4}
\end{aligned}$

Hence,
The required answer is x = $\frac {5}{4}$

~ Hope it helps!

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Ответ:

elizabethxoxo3271

10.01.2023

Mathematics

SAMPLE ANSWER

Step-by-step explanation:

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Solve exponential equation: 2^x * 2^x-2= √2 (picture included)

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