# Tagged Questions

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### solving the equation

let there be a function $f(x)= \ln x-kx^2, k>0$ determine for whihc values of $k$ ,the equation $f(x)=0.5$ has a single solution; attemp to solve: $$0.5 = \ln x-kx^2$$ $$kx^2 +0.5 = \ln x$$ ...
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### Using Chain Rule and Product Rule to find derivative

I have to find the derivative of the following function: $$f(x) = (x^3+ 4)(4x^5 + 2x − 5)^{1/2}$$ To start solving this, I've dissected the equation and realize that I must use the product and chain ...
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### Simplify: $\ln(x^2 − 4)− \ln(x − 2)− \ln 2$

Simplify: $$\ln(x^2 − 4)− \ln(x − 2)− \ln2$$ $$\ln\dfrac{x^2 − 4}{x − 2}− \ln2$$ $$\ln(x + 2)− \ln2$$ $$\ln(x + 2)/2$$ I got this far, is there any other way to simplify it, or do I stop here?
### Solve for $x$: $\frac1e = e^{2x}$
I tried making it to $e^{-1} = e^{2x}$ and had the exponents equal each other $-1=2x$ and the I solved for $x$, making it $x=-1/2$, but that answer is wrong. please help I don't know why that ...