I have two short questions which I think I know the answer-could you please check?
If I write log(b)x - 2log(b)y as a single logarithm it would be log(b) x/y^2, correct? If not please help
and Is the function f(x) = 1/x a exponential function -I think it would be because it could be a number to the negative power, correct or would that be false
Thank you
When you have time,Could someone please check this morning the two problems I listed in the first post along with this one
The function f(x) = logx is a logarthmic function-I think this is false because it should be written as log(then a number)x, correct
Thank you very much
Sure! I'd be happy to help you check your answers. Let's go through each question one by one:
1. To write the expression log(b)x - 2log(b)y as a single logarithm, you can use the properties of logarithms. The power rule states that log(b)(a) - log(b)(c) is equal to log(b)(a/c). So, applying this rule, we can rewrite the expression as log(b)(x) - log(b)(y^2). Then, using the quotient rule, which states that log(b)(a) - log(b)(c) is equal to log(b)(a/c), we get log(b)(x/y^2). Therefore, you are correct!
2. The function f(x) = 1/x is not an exponential function. An exponential function takes the form f(x) = a^x, where a is a constant. In this case, f(x) = 1/x is actually a rational function because it involves division. It represents the reciprocal of x. Exponential functions involve positive powers of a, whereas 1/x involves negative powers. So, your intuition is correct – it is not an exponential function.
I hope this clears things up for you! If you have any more questions, feel free to ask.