7.3 Logarithmic Functions

Question

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

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solve the equation

log₁₀((6c+3)/11)=log₁₀(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

Answer 1

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