Solve $$ \log _{2}(x)=2 $$

1. We start with the equation: $$ \log_{2}(x)=2 $$ 2. Convert the logarithmic equation to its exponential form using the definition of logarithms: $$ \log_{a}(b)=c $$ implies $$ a^c=b $$. Therefore, $$ 2^2 = x $$ 3. Compute $$ 2^2 $$: $$ 2^2 = 4 $$ 4. So, the solution is: $$ x=4 $$ $$ x=4 $$

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Premium

Home Question Bank Math Algebra

Question

Solve

Ask by Moran Barnett. in the United States

Mar 28,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Solution

We start with the equation:
Convert the logarithmic equation to its exponential form using the definition of logarithms:
implies .
Therefore,
Compute :
So, the solution is:

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg

Explain

Simplify this solution

The Deep Dive

To solve

, we can rewrite the logarithmic equation in its exponential form. This means that if

, then

is equal to

raised to the power of

. So, we have:

Calculating that gives us:

Therefore, the solution is

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