URGENT HELP PLEASE Logarithms Growth and Decay

[chameleonkids]

U.S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x)=51.42+(15.473)*log x, where x = 0 is 1980.
b) When will there be 80 million families? I know the answer and how many years time but I need to show work. This is what I have so far 80=51.42+(15.473)*log x

2. The age in years of a female blue whale is approximated by t=-2.57ln(87-L/63)
a) How old is a female whale that measures 80 feet?
b)What is the length of a female blue whale that is 4 years old?

I know the formula for these in the terms of P(t)=Po^ekt

[buddy]

I know the formula for these in the terms of P(t)=Po^ekt

Maybe "P(t) = P₀e^(kt)"? And that's just for exponential growth.

U.S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x)=51.42+(15.473)*log x, where x = 0 is 1980.

This isn't exponential growth, so the formula is different.

b) When will there be 80 million families? I know the answer and how many years time but I need to show work. This is what I have so far
80=51.42+(15.473)*log x

Now subtract the 51.42, divide through by the 15.473, and then raise both sides as powers of 10. Simplify to get the answer.

2. The age in years of a female blue whale is approximated by t=-2.57ln(87-L/63)

a) How old is a female whale that measures 80 feet?

Plug "80" in for "L", and simplify to get the answer for "t".

b)What is the length of a female blue whale that is 4 years old?

Plug "4" in for "t", and solve to get the answer for "L".

[chameleonkids]

Thanks for the help. On the whale question I realize what I should plug in where, my problem is trying to solve it to get the correct answer. I plug the numbers in but do not know how to solve it properly. Does that make sense?

t=-2.57ln(87-80/63)
t=-2.57ln(7/63)
t=5.646 is this correct?

4=-2.57ln(87-L/63)
63*4=-2.57ln(87-L)*63
252=-2.57ln(87-L)
is this going in the right direction? clueless here

thanks so much for the help

[buddy]

Thanks for the help. On the whale question I realize what I should plug in where, my problem is trying to solve it to get the correct answer. I plug the numbers in but do not know how to solve it properly. Does that make sense?

If you don't know about logs and how to work with them, then try studying lessons, like what logs are and how to solve log eqns.

t=-2.57ln(87-80/63)
t=-2.57ln(7/63)
t=5.646 is this correct?

Yes.

4=-2.57ln(87-L/63)
63*4=-2.57ln(87-L)*63

No. You can't go inside a function like that. The 63 is inside the log; you can't take it out like it'smultiplied or something. Try those lessons. Do you know what function notation is?