Evaluate log(Base4) ^3sqrt64 (The ^3 is an exponent infront of sqrt 64)
I keep getting wrong answer :|
ahh i think you mean cube root for that ^3sqrt(64). if so,
log(base4) of (cuberoot(64))
note that we can rewrite cuberoot(64) as cuberoot(4^3) which is equal 4.
log(base4) of 4 = 1
hope this helps~ :)
If the base was 2 then it would be cuberoot 2^6?
yes.
log4 (64)^(1/3)
(1/3) log4 (64)
but log 4(64) = log4(4^3)
so
(1/3)(3) log4(4)
but log4(4) = 1
so
answer = 1
To evaluate log(base4) ^3sqrt(64), we need to understand the different steps involved.
Step 1: Evaluate the cube root of 64.
The cube root of a number means finding the number which, when multiplied by itself three times, gives the original number. In this case, the cube root of 64 is 4 because 4 * 4 * 4 = 64.
Step 2: Write the expression in exponential form.
The expression ^3sqrt(64) can be written as 64^(1/3) because taking the cube root is the same as raising to the power of 1/3. So, 64^(1/3) becomes 4.
Step 3: Evaluate the logarithm expression.
Now, we can evaluate log(base4)(4). The logarithm function asks "what do we raise 4 to in order to get 4?" The answer is 1 because 4^1 = 4. Therefore, log(base4)(4) is equal to 1.
So, the final value of log(base4) ^3sqrt(64) is 1.