Question 1034627
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