Question #0c8b4

1 Answer
Dec 8, 2014

The application of the properties of logarithms is needed here to solve for the value of x.

#log a - log b = log (a/b)#
This is a common logarithm. Therefore, the base is 10

Applying this property,

#log 3(x) - log 3(x+6) = -1#

#log[ (3x)/(3(x+6)]] = -1#

then applying log b = y, which is #10^y = b#

Therefore,

#[(3x)/(3(x+6))] = 10^-1#

take note,# a^-1= (1/a)#

Simplifying,
#(3x)/(3x+18) = 1/10#

then we cross multiply

# 10*3x = 1* (3x+18)#
#30x = 3x +18#

add -3x to both sides

#30x -3x = 3x +( -3x) +18#

then,

#27x = 18#

divide by 27

# x= (18/27)#

reducing to lowest term

#x= 2/3#

we are asked to round off to two decimals. Therefore the answer is #0.67#