Simplify Logarithmic Equations

Question

How to I simplify these two equations for E

1) 8.6 = 2/3log(E/10^4.4)

2) 5.6 = 2/3log(E/10^4.4)

Answer 1

Your constants are not well written so, I've solved it in terms of constants

$$a=b\log \left(\frac{x}{d}\right)$$

$$a\log e=\log \left(\frac{x}{d}\right)^{b}$$ ($e$ is not any arbitrary constant here) $$e^a=\left(\frac{x}{d}\right)^{b}$$

$$d^be^a=x^b$$

$$d^be^a=x^b$$ $$x=de^{a/b}$$ Now just plug in constants