Question
Given log4 ,( 32+x) =3 what is the value of ?
Answers
GPT-4o mini
To solve the equation \( \log_4(32 + x) = 3 \), we can rewrite it in its exponential form. The equation states that \( 32 + x \) is equal to \( 4^3 \).
Calculating \( 4^3 \):
\[
4^3 = 64
\]
Now, we can set up the equation:
\[
32 + x = 64
\]
To find \( x \), we subtract 32 from both sides:
\[
x = 64 - 32
\]
Calculating the right side:
\[
x = 32
\]
Thus, the value of \( x \) is \( \boxed{32} \).
Calculating \( 4^3 \):
\[
4^3 = 64
\]
Now, we can set up the equation:
\[
32 + x = 64
\]
To find \( x \), we subtract 32 from both sides:
\[
x = 64 - 32
\]
Calculating the right side:
\[
x = 32
\]
Thus, the value of \( x \) is \( \boxed{32} \).