Log 96 base 2-2log 6 base 2.
Log 96 base 2-2log 6 base 2
= Log2 (96/6)
= Log2 16
= 4 , since 2^4 = 16
96/36 I think
2 log 6 = log 36
To simplify the expression log 96 base 2 - 2log 6 base 2, we can start by using logarithmic rules.
1. The first rule is the power rule, which states that log a to the power of b is equal to b times log a.
Therefore, we can rewrite the expression as log 96 base 2 - log 6 base 2 squared.
2. The second rule is the subtraction rule, which states that log a - log b is equal to log (a/b).
So, log 96 base 2 - log 6 base 2 squared can be simplified as log (96/6^2) base 2.
3. Next, we simplify the inside of the logarithm. 6 squared is equal to 36, so 96/6^2 is equal to 96/36.
Therefore, log (96/6^2) base 2 can be simplified further to log (96/36) base 2.
4. The final step is to evaluate the expression log (96/36) base 2.
96 divided by 36 is equal to 2.6666... (repeating decimals).
The logarithm base 2 of 2.6666... is approximately 1.442.
Therefore, the simplified expression log 96 base 2 - 2log 6 base 2 is equal to 1.442.
To simplify the given expression, let's break it down step by step:
1. First, let's simplify the expression inside the logarithms. We know that log base 2 of a number x is the power to which we raise 2 to get x. So, we have:
log2(96) - 2 * log2(6)
2. Using the property of logarithms, we can rewrite the expression as:
log2(96) - log2(6^2)
Since 6^2 is equal to 36, we have:
log2(96) - log2(36)
3. Applying the quotient rule of logarithms, we can rewrite the expression as a single logarithm:
log2(96/36)
Simplifying the division inside the logarithm, we have:
log2(2.666...)
4. Finally, we calculate the numerical value of the logarithm using a calculator or any appropriate mathematical software, and we find:
log2(2.666...) ≈ 1.415
Therefore, the simplified value of the given expression, log2(96) - 2log2(6), is approximately 1.415.