Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact ans

Question

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution: log4 (3x+2)=3

Answer 1

log₄ (3x+2) = 3

 

Exponentiate both sides by 4:

4^{log₄ (3x+2)} = 4³

 

Simplify the left side by the definition of logarithm:

3x + 2 = 64

 

3x = 62

 

x = 20.67

 

 

Answer 2

log₄(3x + 2) = 3

 

 

The solution to a logarithm is the exponent of the base number.  The base number is 4.

 

4³ = 3x + 2

 

64 = 3x + 2

 

62 = 3x

 

20.67 = x