SOLUTION: Evaluate the following expression . {{{ 2log(10,5/3) }}} - {{{ log(10 , 7/4) }}} + {{{ 2log(10,3) }}} + {{{ (1/2)log( 10,49) }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Evaluate the following expression . {{{ 2log(10,5/3) }}} - {{{ log(10 , 7/4) }}} + {{{ 2log(10,3) }}} + {{{ (1/2)log( 10,49) }}}      Log On


   

Question 1034627: Evaluate the following expression .
+2log%2810%2C5%2F3%29+ - +log%2810+%2C+7%2F4%29+ + +2log%2810%2C3%29+ + +%281%2F2%29log%28+10%2C49%29+
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your expression is:

2log10(5/3) - log10(7/4) + 2log10(3) + (1/2)*log10(49).

since it's all log10, you can evaluate it as is by using the log function of your calculator.

you will get:

2log(5/3) - log(7/4) + 2log(3) + (1/2)*log(49) = 2.

the log function of your calculator assumes log10, therefore log(x) in the calculator is the same as log10(x).

you could also simplify it and then evaluate it.

2log(5/3) is equal to log((5/3)^2) = log(25/9).
- log(7/4) is equal to - log(7/4).
2log(3) is equal to log(3^2) = log(9).
1/2*log(49) is equal to log(49^(1/2)) = log(7).

the expression becomes:

log(25/9) - log(7/4) + log(9) + log(7).

since log(a) - log(b) = log(a/b), and since log(a) + log(b) = log(a*b), you can simplify this expression to get:

log((25/9*9*7)/(7/4))

you can simplify this to log(100).

this is equal to y if and only if 10^y = 100.
10^y is equal to 100 when y is equal to 2.
therefore:
log(100) = 2