Alan

Divide both sides by 4500:

1.05^n = 5469.78/4500

Take logs of both sides and use the fact that log(x^n) = n*log(x)

n*log(1.05) = log(5469.78/4500)

Divide both sides by log(1.05)

n = log(5469.78/4500)/log(1.05)

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Rewrite it as y = -x/3 + 2

The slope can now be read off directly as -1/3 and the y-intercept as 2

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Have a look at: http://www.mathsisfun.com/metric-imperial-conversion-charts.html 

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Another way of seeing there are no real roots is to rewrite the equation as:

x^4 + 3x^2 + 5 = x

The left-hand side is always greater than or equal to 5, whatever the value of x.

If x is less than 5 the right-hand side is obviously less than 5 and hence less than the left-hand side.

If x is greater than or equal to 5 the x^4 on the left-hand side, on it's own, is greater than the x on the right-hand side.

Hence there are no real values of x that satisfy the equation (i,e. there are no real roots).

See graph:

We can write the ratio as |x - 3|/((x - 3)(x + 3))

As x → 3 from above |x - 3| is just x - 3 , so the ratio becomes 1/(x + 3) or 1/6

As x → 3 from below |x - 3| is 3 - x, so the ratio becomes -1/(x + 3) or -1/6

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None!

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What do you want to do with this?

If you are looking for a specific function, U, and frequency w, that satisfies this, then by setting w = sqrt(5) and

U(t,x) = -sin(wt)cos(x) you get:

U_tt = 5sin(wt)cos(x)  and U_xx = sin(wt)cos(x)  so that  U_tt = 4U_xx + sin(wt)cos(x)

However, you might have had something entirely different in mind!

Known as a googol.

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 x/7.69*10^14 = tan(1)

x = 7.69*10^14*tan(1)

If we assume the 1 means 1 radian, then we have x ≈ 1.19765*10^15

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