exponential and logrithmic function?

Question

q:1if a,b,c are positive numbers in geometric progression,show that loga,logb and logc are in arithmetic progression
q:2 the functions f is given by f:x=log(1+x) where x belongs to real no and x greater than -1.express the definition of f inverse in a similar form.
q:3jacques is saving for a new car which will cost $29000.he saves by putting $400 a month into saving account which gives 0.1% interest per month.after how many months will he be able to buy his car.assume it doesnot increase in price
note down:
answer for q3 is 71
answer for 2 is ex-1
plz solve them for me

Answer 1

1)
a,b,c in GP
b^2 = ac
2 log b = log ac = log a + log c
log b = (log a + log c)/2

This shows logs are in AP.

2 )
The inverse function should be e^x = 1+x ( If using natural log )
i.e. f:x = e^x - 1

I'll try the 3rd one and post later.

Answer 2

The organic exponential function: f(x) = e^x. The graph of it particularly is increasing on its area, it particularly is the whole genuine numbers. The graph is likewise curving upward. the selection is the set of all constructive numbers. It incorporates the ingredient (0,a million). it particularly is asymptotic going to the left to the x-axis. © The organic logarithmic function: f(x) = ln (x) The graph is increasing on its area, it particularly is the set of constructive numbers. The graph is curving downward. the selection is the set of genuine numbers. It incorporates the ingredient (a million,0) it particularly is asymptotic to the y-axis because of the fact the x-values visit 0 from the appropriate.