Write the expression as a single logarithm: 3log(a)-log(b)-(1/2)log(c)
I want to check my answer.
I got log(a^3/bc^(1/2))
correct
thanks Bob :)
SIMPLIFY 2LOG8 MINUS 3LOG2
To write the expression as a single logarithm, you can use the properties of logarithms.
When subtracting logarithms, you can divide the numbers inside the logarithms. And raising a logarithm to a power is the same as multiplying the number inside the logarithm by that power.
1. Start with the expression: 3log(a) - log(b) - (1/2)log(c)
2. Using the properties of logarithms, we can combine the subtraction and division into one term:
3log(a) - log(b) - (1/2)log(c) = log(a^3) - log(b) - log(c^(1/2))
3. Now, apply the property of logarithms that states: log(x) - log(y) = log(x/y):
log(a^3) - log(b) - log(c^(1/2)) = log(a^3/b) - log(c^(1/2))
4. Lastly, apply the property of raising a logarithm to a power:
log(a^3/b) - log(c^(1/2)) = log(a^3/b) - log(c^(1/2)^2) = log(a^3/b) - log(c)
The final expression is log(a^3/b) - log(c).
Comparing it to your answer, log(a^3/bc^(1/2)), we can see that they are not equivalent. The correct answer is log(a^3/b) - log(c).