Problem statement: We need to find the value of log_(2)32. This means we are looking for the power to which the base 2 must be raised to get 32.Equation setup: We know that 2 raised to some power gives us 32. We can write this as 2^x = 32. Now we need to find the value of x.Expressing 32 as a power of 2: We can express 32 as a power of 2. Since 32 is 2 multiplied by itself 5 times, we can write 32 as 2^5.Equating the exponents: Now we have 2^x = 2^5. Since the bases are the same, the exponents must be equal. Therefore, x must be 5.Final result: So, log_(2)32 is equal to 5. This is because 2 raised to the power of 5 gives us 32.

Grade 8

Relationship between squares and square roots

Full solution

\log _{2} 32=

Problem statement: We need to find the value of $\log_{2}32$ . This means we are looking for the power to which the base $2$ must be raised to get $32$ .
Equation setup: We know that $2$ raised to some power gives us $32$ . We can write this as $2^x = 32$ . Now we need to find the value of $x$ .
Expressing $32$ as a power of $2$ : We can express $32$ as a power of $2$ . Since $32$ is $2$ multiplied by itself $5$ times, we can write $32$ as $2^5$ .
Equating the exponents: Now we have $2^x = 2^5$ . Since the bases are the same, the exponents must be equal. Therefore, $x$ must be $5$ .
Final result: So, $\log_{2}32$ is equal to $5$ . This is because $2$ raised to the power of $5$ gives us $32$ .