Pre-calculus questions

Question

Atmospheric pressure P in pounds per square inch is represented by the formula P= 14.7e^-0.21x , where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with the atmospheric pressure of 8.719 pounds per square inch?( hint : there are 5, 280 feet in a mile)

I need help with explaining the process for the answers on all of these questions to rely that process as clearly as possible and as simple as possible.

Question 2:

Use the one-to-one property of logarithms to solve:

Ln(x^2-10)+ln(9)= ln (10)

Enter the exact answers

Last question:

Condense the expression to a single logarithm using the properties of logarithms.

Log(x)-1/2 log(y)+3log(z)

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c×log(h)

Answer 1

×1)

P=14.7e^-0.21x

P=14.7e^-0.21x

-0.21x=ln(P/14.7)

x = ln(P/14.7)/-0.21

Let P =8.719 and solve for x then multiply by 5280 and round to nearest foot.

2)

ln(x²-10)+ln(9)=ln(10)

ln(x²-10)=ln(10)-ln(9) = ln(10/9)

e^{ln(x^2-10)}=e^ln(10/9)

x²-10= 10/9

x = √(10+10/9)

3)

Using alog(b)=log(b^a)

log(x) - log(y^1/2)+log(z³)

Use log(a)-log(b)= log(a/b) and log(a)+log(b)= log(a×b)

log(x×z³/y^1/2)=log(x×z³/√y)