Simplify log2(8)+log2(2) into single logarithm
since 16=2^4, log2(16) = 4
also, log2(8)+log2(2) = 3+1 = 4
Yes, that's correct! We can also simplify the expression using the fact that log2(8) = 3 and log2(2) = 1, and thus:
log2(8) + log2(2) = 3 + 1 = 4
Either way, we get the same result: log2(8) + log2(2) = log2(16) = 4.
To simplify log2(8) + log2(2) into a single logarithm, we can use the properties of logarithms.
First, let's write the given expression using the rules of logarithms:
log2(8) + log2(2) = log2(8 * 2)
Next, we can simplify the expression inside the logarithm:
log2(8 * 2) = log2(16)
Finally, since the base of the logarithm is 2 and we need to express the logarithm in terms of a single logarithm, we can write the simplified form as:
log2(16) = log2(2^4)
Using the rule that log base a (a^n) = n, we can rewrite the expression as:
log2(2^4) = 4
Therefore, log2(8) + log2(2) simplifies to 4.
Using logarithmic rules, we can simplify this expression:
log2(8) + log2(2) = log2(8 x 2)
Simplifying the expression within the logarithm, we get:
log2(16)
Therefore, log2(8) + log2(2) = log2(16)