4 log 8/25 3 log 16/125 log 5.?

Question

Answer

Solution

We are given the expression as 4 log 8/25 + 3 log 16/125 + log 5.

Step 1: Convert the given logarithms to base 10

We know that the common logarithm is the logarithm to the base 10, so we will convert the given logarithms to base 10.

4 log 8/25 = 4 log (8/25) / log 10 = 4 log (2^3 / 5^2) / log 10 = 4 [(3 log 2 - 2 log 5) / log 10] = 4 [0.903 - 0.602] = 1.204

3 log 16/125 = 3 log (16/125) / log 10 = 3 log (2^4 / 5^3) / log 10 = 3 [(4 log 2 - 3 log 5) / log 10] = 3 [0.602 - 0.903] = -0.903

log 5 = log 5 / log 10 = 0.699

Step 2: Substitute the values in the given expression

Now, we will substitute the values in the given expression.

4 log 8/25 + 3 log 16/125 + log 5 = 1.204 - 0.903 + 0.699 = 0.999

Step 3: Simplify the expression

We can simplify the expression as follows:

4 log 8/25 + 3 log 16/125 + log 5 = log (8/25)^4 + log (16/125)^3 + log 5 = log [(8/25)^4 (16/125)^3 5] = log 1 = 0

Final Answer

Therefore, the value of the given expression is 0.

Answer

Maybe 32/625
am I right,
if yes then please reply