^{x}

_{10}((6c+3)/11)=log

_{10}(3c/5)

_{ }

Which is the inverse of f(x)=3^{x}

-----------------------------------

solve the equation

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

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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

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

f(x) = 3^{X}

f^{-1}(x ) = log 3

log ( 6c +3 ) /11 = log 3c/ 5

If the log of 2 expressions are equal, then the argument of the log function has to be equal.

6c + 3 / 11 = 3c /5

5( 6c + 3) = 33 c

30c + 15 = 33c

3c = 15

c = 15/3 = 5

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## 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.