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PSYCHO15rus [73]
2 years ago
14

Please help meeee ………..

Mathematics
1 answer:
Len [333]2 years ago
6 0

Answer:

  x = 5

Step-by-step explanation:

The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.

<h3>Application</h3>

  \dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}

__

<em>Additional comment</em>

Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.

  \log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5

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