find the value of 81 (1/ log base5 rash to 3 +27 log base 9 rash to 36 +3 ( 4/log base 9 rash to 9
To find the value of the expression, we need to evaluate the given logarithmic expressions.
Let's start with the first term: 1/log base 5 of rash to 3.
To evaluate this, we need to rewrite the expression using the change-of-base formula. The change-of-base formula states that log base b of x = log base a of x / log base a of b.
So, 1/log base 5 of rash to 3 = log base rash to 3 / log base 5 of rash.
Now, let's move on to the second term: 27 log base 9 of rash to 36.
Again, we can use the change-of-base formula to rewrite the expression. 27 log base 9 of rash to 36 = 27 log base rash to 36 / log base rash to 9.
Finally, let's evaluate the last term: 4/log base 9 of rash to 9.
We can once again apply the change-of-base formula: 4/log base 9 of rash to 9 = 4 log base rash to 9 / log base rash to 9.
Now that we have converted all the logarithmic expressions into the same base, which is "rash," we can add them together:
1/log base 5 of rash to 3 + 27 log base 9 of rash to 36 + 4/log base 9 of rash to 9
= log base rash to 3 / log base 5 of rash + 27 log base rash to 36 / log base rash to 9 + 4 log base rash to 9 / log base rash to 9
= (log base rash to 3 * log base rash to 9 + 27 log base rash to 36 + 4 log base rash to 9) / log base 5 of rash
Now, simplify the expression within the parentheses:
= (log base rash to (3 * 9) + log base rash to (36^27) + log base rash to (9^4)) / log base 5 of rash
= (log base rash to 27 + log base rash to 972 + log base rash to 6561) / log base 5 of rash
Since all three logarithms have the same base (rash), we can combine them:
= log base rash to (27 * 972 * 6561) / log base 5 of rash
= log base rash to (17,576,904,352) / log base 5 of rash
Now, to find the value of 81 multiplied by the expression we obtained, we can evaluate:
81 * log base rash to (17,576,904,352) / log base 5 of rash
Please note that without an actual value or specific information about "rash," we cannot compute the final result.