Answer :
To find the value of \( x \) in the logarithmic equation \( \log_2(32) = x \), we can use the properties of logarithms and exponents.
1. Understanding the logarithmic equation:
[tex]\[ \log_2(32) = x \][/tex]
This equation means: "To what power must 2 be raised, to obtain 32?"
2. Rewriting the equation in exponential form:
[tex]\[ 2^x = 32 \][/tex]
3. Recognizing powers of 2:
To solve this, identify that \( 32 \) is a power of 2. Specifically,
[tex]\[ 32 = 2^5 \][/tex]
4. Matching the exponents:
Given that \( 2^x = 32 \) and also \( 32 = 2^5 \), we can see that:
[tex]\[ 2^x = 2^5 \][/tex]
5. Equating the exponents:
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ x = 5 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( \log_2(32) = x \)[/tex] is [tex]\( \boxed{5} \)[/tex].
1. Understanding the logarithmic equation:
[tex]\[ \log_2(32) = x \][/tex]
This equation means: "To what power must 2 be raised, to obtain 32?"
2. Rewriting the equation in exponential form:
[tex]\[ 2^x = 32 \][/tex]
3. Recognizing powers of 2:
To solve this, identify that \( 32 \) is a power of 2. Specifically,
[tex]\[ 32 = 2^5 \][/tex]
4. Matching the exponents:
Given that \( 2^x = 32 \) and also \( 32 = 2^5 \), we can see that:
[tex]\[ 2^x = 2^5 \][/tex]
5. Equating the exponents:
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ x = 5 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( \log_2(32) = x \)[/tex] is [tex]\( \boxed{5} \)[/tex].
