To solve the equation [tex]\(3 = \log_2 x\)[/tex], we need to find the value of [tex]\(x\)[/tex]. Here's a step-by-step solution:
1. Understand the Logarithmic Equation:
The equation [tex]\(3 = \log_2 x\)[/tex] is in the form of a logarithm, where the base is [tex]\(2\)[/tex] and the result of the logarithm is [tex]\(3\)[/tex].
2. Rewrite in Exponential Form:
Recall that a logarithmic equation [tex]\( \log_b (a) = c \)[/tex] can be rewritten as an exponential equation [tex]\( b^c = a \)[/tex]. For our specific equation:
[tex]\[
3 = \log_2 x
\][/tex]
This can be rewritten as:
[tex]\[
2^3 = x
\][/tex]
3. Calculate the Value of [tex]\(x\)[/tex]:
Now we simply calculate [tex]\( 2^3 \)[/tex]:
[tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
4. Conclusion:
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(3 = \log_2 x\)[/tex] is:
[tex]\[
x = 8
\][/tex]
So, the final solution to the equation [tex]\(3 = \log_2 x\)[/tex] is [tex]\( x = 8 \)[/tex].
