X= log 3 5 * log 4 27 * log 3 sqrt 2 25

ok. what, you want a simpler numeric value for x?

All those spaces are confusing, but if you mean

log_3(5) * log_4(27) * log_3(√225)
that is kinda weird. I suspect a typo. So, using base 3 logs all the way, I get

log5*log27*log15
=4log3*2log5

since log_3(3) = 1, that is just

2log5 or log25

Most calculators don't have a log_3 button, so change the base to 10 or e (does not matter which):

log_3(25) = log25/log3

To solve the expression X = log₃₅ * log₄₂₇ * log₃√₂₂₅, we can start by evaluating each logarithm separately and then multiplying the results.

Step 1: Evaluate log₃₅
To evaluate log₃₅, we need to find the power to which 3 must be raised to get 35. In other words, we're looking for the exponent x in the equation 3^x = 35.

Since 3^2 = 9 and 3^3 = 27, we know that 3 is between 2 and 3. Therefore, x will be slightly more than 2, but less than 3. We can estimate that x is approximately 2.5.

So, log₃₅ ≈ 2.5.

Step 2: Evaluate log₄₂₇
To evaluate log₄₂₇, we need to find the power to which 4 must be raised to get 427. In other words, we're looking for the exponent y in the equation 4^y = 427.

Since 4^3 = 64 and 4^4 = 256, we know that 4 is between 3 and 4. Therefore, y will be slightly more than 3, but less than 4. We can estimate that y is approximately 3.5.

So, log₄₂₇ ≈ 3.5.

Step 3: Evaluate log₃√₂₂₅
To evaluate log₃√₂₂₅, we need to find the power to which 3 must be raised to get the cube root (√₃) of 225. In other words, we're looking for the exponent z in the equation 3^z = √₃²²⁵.

Since 3^3 = 27 and 3^4 = 81, we know that 3 is between 3 and 4. Therefore, z will be slightly more than 3, but less than 4. We can estimate that z is approximately 3.3.

So, log₃√₂₂₅ ≈ 3.3.

Step 4: Calculate X
Now that we have found the values of log₃₅, log₄₂₇, and log₃√₂₂₅, we can multiply them together to find the value of X.

X ≈ log₃₅ * log₄₂₇ * log₃√₂₂₅
≈ 2.5 * 3.5 * 3.3
≈ 28.875

So, X ≈ 28.875.