Log6 1296
3
4
-4
6
Log6 1296 = x.
6^x = 1296,
x*Log 6 = Log1296,
X = Log1296/Log6 = 4.
let Log6 1296 = x
then ...
6^x = 1296
try some powers of 6.
e.g. 6^2 = 36
6^3 = 216
....
To find the logarithm of 1296 with base 6, we need to determine the exponent to which 6 must be raised to get 1296.
Step 1: Logarithm of 1296 with base 6
log6 1296
Step 2: Write the equation
6^x = 1296
Step 3: Solve for x
Let's solve the equation 6^x = 1296 using different values of x:
For x = 3:
6^3 = 6 * 6 * 6 = 216, which is not equal to 1296.
For x = 4:
6^4 = 6 * 6 * 6 * 6 = 1296.
Therefore, the value of x that makes 6^x equal to 1296 is x = 4.
Answer: log6 1296 = 4.
To calculate the logarithm of 1296 to the base 6, you can use the logarithmic identity:
log base b (x) = log base c (x) / log base c (b)
In this case, we want to calculate log base 6 (1296), so we can rewrite it as:
log base 6 (1296) = log base 10 (1296) / log base 10 (6)
To calculate log base 10 (1296), simply take the logarithm of 1296 to the base 10 using a scientific calculator or math software. The result is 3.110.
Now, let's calculate log base 10 (6). This gives us 0.778.
Next, divide log base 10 (1296) by log base 10 (6):
log base 6 (1296) = 3.110 / 0.778
This simplifies to:
log base 6 (1296) ≈ 3.99222
Therefore, the logarithm of 1296 to the base 6 is approximately 3.99222.
Now, let's calculate the logarithm of 3, 4, -4, and 6 to the base 6 using the same method:
log base 6 (3) ≈ 0.63093
log base 6 (4) ≈ 1
log base 6 (-4) is undefined because logarithms of negative numbers are not defined in the real number system.
log base 6 (6) = 1
To summarize:
log base 6 (3) ≈ 0.63093
log base 6 (4) ≈ 1
log base 6 (-4) is undefined
log base 6 (6) = 1