We know that log base 10 of 2 is x, which means that 10 to the power of x is equal to 2.
To express log base 10 of 12.5 in terms of x, we need to find a way to write 12.5 in terms of 2 and x. We can write 12.5 as 10 to the power of 1.09691 (approximately) using a calculator.
Now, we can use the laws of logarithms to simplify the expression:
log base 10 of 12.5 = log base 10 of (10^1.09691)
= 1.09691 * log base 10 of 10
= 1.09691
Therefore, we want to find an expression among the given options that equals 1.09691 when x is substituted into it.
We can check each option by substituting x into it and simplifying:
: 2(1 + x) = 2 + 2x
Substituting x = log base 10 of 2 gives 2 + 2(log base 10 of 2), which does not equal 1.09691.
: 2 + 3x
Substituting x = log base 10 of 2 gives 2 + 3(log base 10 of 2), which also does not equal 1.09691.
: 2(1 - x) = 2 - 2x
Substituting x = log base 10 of 2 gives 2 - 2(log base 10 of 2), which also does not equal 1.09691.
: 2 - 3x
Substituting x = log base 10 of 2 gives 2 - 3(log base 10 of 2), which equals 1.09691.
Therefore, the correct answer is: 2 - 3x.