The value of log2√3 1728=
I will assume you meant 2√3 to be the base, that is, you want log<sub)2√3 1728
let x = log<sub)2√3 1728
(2√3)^x = 1728
2√3 = 1728^(1/x)
square both sides
12 = 1728^(2/x) , but 12^3 = 1728
12 = 12^(6/x)
so 6/x = 1
x = 6
This is probably not the easiest way to do it, but I just followed the flow
Since 2√3 = √12, you have
log√1212^3
= 3log√1212
= 3*2
= 6
To find the value of log2√3 1728, we need to understand the properties of logarithms and evaluate it step by step.
First, let's simplify the expression: √3 1728.
Step 1: Simplify the inside of the square root.
√3 1728 = √(3 * 1728)
Step 2: Simplify the numbers under the square root.
√(3 * 1728) = √(5184)
Step 3: Evaluate the square root.
√(5184) = 72
Now that we have simplified √3 1728 to 72, we can proceed to calculate the logarithm.
The given expression is log2(72).
To calculate this, we need to remember that log2(x) represents the logarithm of x to the base 2. In other words, we need to find the power to which 2 must be raised to equal 72.
Let's calculate it step by step:
Step 1: Let n be the power to which 2 must be raised to equal 72.
2^n = 72
Step 2: Solve for n by using the logarithm property:
n = log2(72)
Step 3: Calculate the value of n using a calculator or other appropriate methods.
Using a calculator, we find that log2(72) is approximately equal to 6.169925.
Therefore, the value of log2√3 1728 is approximately 6.169925.