Solve for x. Round to the nearest thousandth if necessary.

Question

log₄ x + log₄ 2 = 3

Answer 1

Log₄ x + Log₄ 2 = Log₄ 2x = 3

So 4³ = 2x

2x = 64

x = 32

Check ....

Log₄ 32 + Log₄ 2 = 3

Log₄ (16*2) + Log₄ 2 = 3

Log₄ 16 + Log₄ 2 + Log₄ 2  = 3

2 + 1/2 + 1/2 = 3

3 = 3  checks okay

 

 

 

Answer 2

log(2x) = 3

 

raising both sides to the power base 4,

 

2x = 4^3

 

x = 4^3/2 = 4*4*4/2 = 32

 

check log(64) = 3 because 4^3 = 4*4*4