Thread: How to solve equation contain logarithm

1. How to solve equation contain logarithm

How to solve this equation:

4827/t +7log_10(t)-27=0

2. Hy. You can solve it by using the Lambert-W function by first writing it as:

$\frac{4827}{t}+7\log_{10} t=27$

$\frac{4827}{t}+\frac{7}{\ln(10)}\ln(t)=27$

or just look at:

$\frac{a}{t}+b\ln(t)=c$

Now, in order to get it into a form to use W, you need to put it in the form:

$k=f(t)e^{f(t)}$

then taking W I get:

$f(t)=W(k)$

So try and do some algebra to get:

$-\frac{a}{b}e^{-c/b}=-\frac{a}{bt}e^{-\frac{a}{bt}}$

then take W right?