How do you solve this log equation?

Question

Solve for x to two decimal places: 5000(1.09^12x) = 9500

Answer 1

5000(1.09^12x) = 9500
12x(In1.09)=In(1.9)
12x=In(1.9-1.09)
12x=In0.81
x=(In0.81)/12

Answer 2

There are a couple of steps to solve this equation:

Step 1- (1.09^12X) = 9500/5000 (divide by 5000 on both sides).

Step 2 - Log(1.09^12X) = Log(9500/5000) (Multiply by log on both sides).

For step three it is important to know this property of log function. Log(A^X) = X Log(A).

Step 3 - 12X Log(1.09) = Log(9500/5000).

Step 4 - X= Log(1.9) / 12 Log(1.09)

Answer 3

Rewrite:
1.09^(12x) = 9500/5000 = 95/50 = 19/10
Use log[10]
Take log of both sides
12x log[10]1.09 = log[10]19 - log[10]10 = log[10]19 - 1
12x = {log[10]19 -1}/log[10]1.09
x = {log[10]19 - 1}/(12)(log[10]1.09)

Answer 4

The general idea goes something like below...

5000(1.09^12x) = 9500
1.09^12x = 1.9
ln(1.09^12x) = ln(1.9)
12x * ln(1.09) = ln(1.9)
12x = ln(1.9)/ln(1.09)
12x = 0.6419/0.0862 = 7.4480
x = 0.6207

Answer 5

(1.09^12x)= 9.500/5.000=1.9If you take log

12xlog(1.09)=log1.9

x=log1.9/(12*log 1.09)=0.621

Answer 6

ab^(cx) = d
b^(cx) = d/a
Ln(b^(cx)) = d/a
cx = d/(aLn(b))

x = d/(acLn(b))