Answer:
Explanation:
We can start by using the logarithmic rule that states:
log a (mn) = log a (m) + log a (n)
And also the property:
log a (b^c) = c*log a (b)
With these rules, we can simplify the given expression as follows:
log4 n = 1/4 log4 81 + 1/2 log4 25
log4 n = log4 81^(1/4) + log4 25^(1/2) (using the above properties)
log4 n = log4 (3^4)^(1/4) + log4 (5^2)^(1/2) (81 = 3^4 and 25 = 5^2)
log4 n = log4 3 + log4 5 (using the rule log a (b^c) = c*log a (b))
log4 n = log4 (3*5) (using the rule log a (mn) = log a (m) + log a (n))
log4 n = log4 15
Therefore, the solution to the equation log4 n=1/4 log4 81 + 1/2 log4 25 is:
n = 15