Question

what do i type in my calculater to solve f(x) = log0.3^x

Answer 1

Just to be clear, is that \[f(x)=\log_{0.3}(x)\]or\[f(x)=\log(0.3^x)\]

Answer 2

the second one

Answer 3

Note that by the properties of logarithms that \[f(x)=\log(0.3^x)=x\cdot \log(0.3)\]

Answer 4

Now suppose you were given that function, with \(y=12\). How would we solve that?\[12=\log(0.3^x)=x \log(0.3)\]So\[x={12 \over \log(0.3)}\]Now look at your calculator. It should have a button that says "log."

Enter 12, hit the division symbol, hit the log button, and enter 0.3 in the parentheses the log should provide you with.

Answer 5

For that example, I'm getting a solution of \(x\approx -22.9499\)