Log Problems

Question

I am having a lot of difficulty with these two types of problems, please help

1. 18log26(x)=log26(110)

 

2. (solve each equation, and leave in exact form):

log2(x+4)−log2(x−2)=2

Answer 1

1)

 

18log₂₆(x) = log₂₆(110)

 

 

18 becomes the exponent of x on the left side of equation.

 

log₂₆(x¹⁸) = log₂₆(110)

 

 

Since both sides of the equation have the same log bases, we only need to equate the arguments of the logs.

 

x¹⁸ = 110

 

 

Solve this equation for x by taking the 18th root on both sides of the equation.

 

 

2)

 

log₂(x + 4) - log₂(x - 2) = 2

 

 

Use the properties of logs on the left side.  Since we are subtracting the logs of common bases, we divide their arguments.

 

log₂[(x + 4) / (x - 2)] = 2

 

 

The solution to a log is the exponent of the log's base number.

 

2² = (x + 4) / (x - 2)

 

4 = (x + 4) / (x - 2)

 

 

Solve the equation for x.

 

 

Answer 2

I will work the second one out for you

 

log₂ (x+4) / ( x - 2) = 2

 

(x+4) / (x-2) = 2

 

 

x + 4 = 2x - 4

 

 

x = 8