Solving Exponential Equations Using Logarithms.?

Question

Solve the following equations showing all your work. Round to 3 decimal places.

2^x = 30

5^x - ^1 = 3^x

3.53^x + ^1 = 65.4

16^x - ^4 = 3^3 - ^x

7^x - ^2 = 5^x

Answer 1

1.  2^x = 30

Take the natural log of each side.

x ln(2) = ln(30)

x = ln(30)/ln(2)

Now pull out your calculator and evaluate.

If you don't have a calculator, then http://www.google.com will do it for you... just type it in the search bar.

http://www.google.com/search?q=ln%2830%2...

2.  I'm not sure what you mean by putting ^ in front of the 1?

Does that mean it is part of the exponent?

If so, then you should write it like this 5^(x-1) = 3^x.

Take the natural log of each side.

(x-1) ln(5) = x ln(3)

x ln(5) - ln(5) = x ln(3)

x ln(5) - x ln(3) = ln(5)

x(ln(5)-ln(3)) = ln(5)

x = ln(5)/(ln(5)-ln(3))

The other ones are similar.