1 2500 is invested in an account at interest rate r compound

1). $2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.) r = 0.0570 (2).

Condense the expression to a logarithm of a single quantity.

log_x - 2log_y + 3log_{z (3).}

Use the properties of logarithms to simplify the expression.

log₂₀ 20^{9 (4).}

Use the One-to-One property to solve the equation for x.

log₂(x+4) = log₂ 20

Solution

1)  

If Compounded Continuously Interest: is calculated by the formula then we use another formula:

A(t) = P e^rt

P = 2500 ; r = 0.0570

Time for the amt to double:

2*2500 = 2500e^(0.0570t)

2 =e^(0.0570t)

Taking natural log on both sides:

ln2 = 0.0570t

t = 12.16 years

2) log_x - 2log_y + 3logz

Use the log property : logA +logB -logC = log(A*B/C) and a*logx = log(a^x)

So,logx - 2logy + 3logz =   logx -log(y^2) +log(z^3)

                                  = log ( x*y^2z^3

3) log₂(x+4) = log₂ 20

we can equate the arguments on both side pf log as base is same:

(x+4) = 20

x = 16