Pures maths help needed.

[acroviak]

Hey again.

Couple more pure maths queries!

1. Show that y=ln(x^2 + 5) can be rewritten as x^2 = e^y - 5

2. The root of the equation sin-1(x) = 0.25x + 1 is A. Show that 0.5 > A > 1


The second one i have not got a clue on, so thats the one i need most help with.

Thanks in advance

[acroviak]

any help?

[acroviak]

please?

[bibblebub]

1 remember what ln() means and so take e^() each side of the equation; then re-arrange

[scotman]

1. y = ln(x^2 + 5) Note the Natural logarithm to base e is used here

get rid of logarithm first giving

e^y = x^2 + 5

then -5 to both sides giving

e^y - 5 = x^2

voila

[bibblebub]

2. rearrange this as a function: f(x) = sin-1(x) - 0.25x - 1

find the values of this function for x = 0.5 and x = 1
you will find that one of those is positive and the other is negative
so the point at which f(x) = 0 occurs within that range of value of x

(you could do a rough plot of the graph of x to demonstrate that there is only one root within that range)

[bibblebub]

^^^ should read: ...plot of the graph of f(x)...

[factor-fiction]

1. y= ln k can be written as e^y= k
So y = ln (x^2 +5) can be written as e^y = x² + 5. Simply rearrange then to get the required result.

[acroviak]

Thanks for all the answers! Helped alot!