Which is the inverse of f(x)=3

^{x}-----------------------------------

solve the equation

log

_{10}((6c+3)/11)=log_{10}(3c/5)_{ }---------------------------------------

in astronomy the observed brightness of stars is called apparent magnitude. two stars can be compared using the formula d=2.5logr, where d us the difference of the apparent magnitude of the two stars and r is their brightness ratio. The brightest star Sirius A has an apparent magnitude of -1.46. Alpha Centauri has an apparent magnitude of -2.9.

1) find the difference between the apparent magnitude if Sirius A and Alpha Centauri

2) Find the brightest ratio of the two stars to the nearest tenth

## Comments

^{-1}(x).^{-1}(x) without defining a new function, which we call logarithm. y = f^{-1}(x) = log_{3}(x), which contains all the information as x = 3^y, i.e., the number, x, the base, 3, and the exponent, y.