Log 1728 to the base √3
since √3 = 3^(1/2)
log√31728 = 2log31728
now, 1728 = 12^3 = 2^3 * 3^3 so
2log31728 = 2(log32 + 3)
Not sure just where you're going with this
oops. That would be
2(3log32 + 3)
1728 = 12^3 = 4^3 * 3^3
etc
To calculate log 1728 to the base √3, we can use the change of base formula. This formula states that the logarithm of a number to a certain base can be calculated by dividing the logarithm of that number to another base.
Step 1: Find the logarithm of 1728 to any base.
You can choose any base for this step, but it's typically easiest to use a common base like 10 or e (natural logarithm). Let's use base 10 for this example.
log(1728) = ?
To calculate this logarithm, you can use a scientific calculator or software that has a logarithm function. On most calculators, the logarithm function is denoted as "log" or "log10".
log(1728) = 3.235
(Note: This value is rounded to three decimal places)
Step 2: Find the logarithm of the base √3 to the same base chosen in step one.
We chose base 10 in step one, so we need to find log(√3) using base 10.
log(√3) = ?
Similarly, you can use a scientific calculator or software to find the logarithm.
log(√3) ≈ 0.301
(Note: This value is rounded to three decimal places)
Step 3: Apply the change of base formula.
Now that we have the logarithms of 1728 and √3 to the same base, we can use the change of base formula:
log base √3 of 1728 = log(1728) / log(√3)
log base √3 of 1728 ≈ 3.235 / 0.301 ≈ 10.76
Therefore, log 1728 to the base √3 is approximately equal to 10.76.