Solve
(log base 2, cube root of 2)
log2(2^1/3)
You transform it into the form above, right? then you cancel the 2s to get 1/3
right answer, wrong reason.
You don't "cancel" the 2's. You evaluate the log function. By definition (using bas 2),
2^(log x) = x
That is, the log of a number is the power of the base you need to get that number.
So, log 2^x = x*log 2 = x*1 = x
To solve the expression log(base 2, cube root of 2), we can follow these steps:
Step 1: Start with the expression log(base 2, cube root of 2).
Step 2: Use the logarithmic identity log(base b, c) = log(base a, c)/log(base a, b) to rewrite the expression as log(base 2, 2^(1/3))/log(base 2, 2).
Step 3: Simplify the numerator. The cube root of 2 can be written as 2^(1/3). Therefore, the expression becomes log(base 2, 2^(1/3))/log(base 2, 2).
Step 4: Apply the logarithmic property which states that log(base b, b) = 1. Therefore, the expression becomes 1/3.
So, the solution to log(base 2, cube root of 2) is 1/3.