LOG(base5)(3/5)+3log(base5)(15/2)-log(base5)(81/8)
Maybe there is an easier way, but that was fun !
sorry I don't understand
Log5(3/5)+3log5(15/2)-log5(81/8)
Solution
Log5(3/5)×log5(15^3/2^3)
=Log5(3/5×3375/8)
=Log5(2025/8)/log5(81/8)
=Log5(2025/81)
=Log5(25)
=Log5(5^2)
=Therefore Log5(3/5)+3log5(15/2)-log5(81/8)=2log5(5)
To simplify the expression LOG(base5)(3/5) + 3log(base5)(15/2) - log(base5)(81/8), we can start by using the properties of logarithms.
1. First, let's simplify the logarithm of the fractions. Remember that the logarithm of a fraction is the logarithm of the numerator minus the logarithm of the denominator:
log(base5)(3/5) = log(base5)(3) - log(base5)(5)
log(base5)(15/2) = log(base5)(15) - log(base5)(2)
log(base5)(81/8) = log(base5)(81) - log(base5)(8)
2. Next, we can use the power rule of logarithms to simplify the terms with exponents:
log(base5)(3) = log(base5)(3)
log(base5)(15) = log(base5)(3 * 5) = log(base5)(3) + log(base5)(5)
log(base5)(81) = log(base5)(3^4) = 4 * log(base5)(3)
log(base5)(8) = log(base5)(2^3) = 3 * log(base5)(2)
3. Now, substitute these simplified forms back into the original expression:
log(base5)(3/5) + 3log(base5)(15/2) - log(base5)(81/8)
= (log(base5)(3) - log(base5)(5)) + 3((log(base5)(3) + log(base5)(5)) - (4 * log(base5)(3) - 3 * log(base5)(2)))
= log(base5)(3) - log(base5)(5) + 3log(base5)(3) + 3log(base5)(5) - (4 * log(base5)(3) - 3 * log(base5)(2))
4. Simplify further using algebraic properties:
log(base5)(3) - log(base5)(5) + 3log(base5)(3) + 3log(base5)(5) - (4 * log(base5)(3) - 3 * log(base5)(2))
= (1 + 3 - 4) * log(base5)(3) + (3 + 3) * log(base5)(5) + 3 * log(base5)(2)
= 0 * log(base5)(3) + 6 * log(base5)(5) + 3 * log(base5)(2)
= 6 * log(base5)(5) + 3 * log(base5)(2)
Therefore, the simplified form of LOG(base5)(3/5) + 3log(base5)(15/2) - log(base5)(81/8) is 6 * log(base5)(5) + 3 * log(base5)(2).
log5 [ (3/5)(15^3/8) / (81/8)]
well at least the 8 goes away easy
log5 [ 3 *225 * 3 / 81 ]
log5 [ 225/9 ]
2 log 5 (15/3)
LOL !!!
2 log5 (5)
2 :)