Question
4log
2
(x)+7=7
2
(x)+7=7
Answers
GPT-4o mini
To solve the equation
\[
4\log_2(x) + 7 = 7,
\]
we can start by isolating the logarithmic term. Subtract 7 from both sides:
\[
4\log_2(x) = 0.
\]
Next, divide both sides by 4:
\[
\log_2(x) = 0.
\]
Now, we can convert the logarithmic equation to its exponential form. Recall that \(\log_b(a) = c\) means \(b^c = a\). Therefore, from \(\log_2(x) = 0\), we have:
\[
x = 2^0.
\]
Since \(2^0 = 1\), we find:
\[
x = 1.
\]
Thus, the solution to the equation is
\[
\boxed{1}.
\]
\[
4\log_2(x) + 7 = 7,
\]
we can start by isolating the logarithmic term. Subtract 7 from both sides:
\[
4\log_2(x) = 0.
\]
Next, divide both sides by 4:
\[
\log_2(x) = 0.
\]
Now, we can convert the logarithmic equation to its exponential form. Recall that \(\log_b(a) = c\) means \(b^c = a\). Therefore, from \(\log_2(x) = 0\), we have:
\[
x = 2^0.
\]
Since \(2^0 = 1\), we find:
\[
x = 1.
\]
Thus, the solution to the equation is
\[
\boxed{1}.
\]