Log problems and solving

Question

Leave as a simplified fraction 

a) 3=log sub 9(x/729)

b)log sub 4y=1/3log sub 4(1728) - log sub 4(8)+log sub 4(14)

c) write in log form: e^.23=1.259

Answer 1

a)

 

3 = log₉(x/729)

 

 

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

 

9³ = x / 729

 

729(9³) = x

 

(9³)(9³) = x

 

9⁶ = x

 

 

b)

 

log₄y = (1/3)log₄(1728) - log₄(8) + log₄(14)

 

 

Compact the right side of the equation using properties of logs.

 

log₄y = log₄(1728^1/3 * 14 / 8)

 

log₄y = log₄(12 * 12 / 8)

 

log₄y = log₄(144/8)

 

 

Equate arguments.

 

y = 144/8

 

y = 18

 

 

c)

 

e^0.23 = 1.259

 

ln(1.259) = 0.23