1. solve for x. logx+log(x-1)=log(4x) 2. solve for x. write your answer to three decimal places. (l000)(1.05)^3x=3000 3. solve for t. write your answer to three decimal places. 25000=500e^.06t

Step-by-step explanation:

log(x) + log(x-1) = log(4x)  

The numbers that are separated by a plus sign (or a minus sign) can be combined as multiplication.

log5 + log10 = log50. You can try this yourself. log(5) + log(10) - log(50) = 0

So log(x) + log(x-1) = log(4x)

log(x)(x - 1) = log(4x)    When you take the antilog of both sides, you get

(x)(x - 1) = 4x                 Remove the brackets

x^2 - x = 4x                  Subtract 4x from both sides.

x^2 - x - 4x = 4x - 4x   Combine like terms.

x^2 - 5x = 0                Use the distributive law to take out the common factor

x(x - 5) = 0

This means there are two answers

x = 0

x - 5 = 0

x = 5

x = 0 gives an error, so it is not a solution.

x = 5 gives 1 solution

Check

log(5) + log(5 -1) = log(4*5)

log(5) + log(4) = log(20)

0.6989 + 0.6021 = 1.3010

1.03010 = 1.3010

x^2 - 5x = 0