If (3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c , what is c in terms of a and b ? A. a + b - 2 B. a + b + 2 C. (a + b)/2 D. ab - 2 E. ab + 2 M46-06

multiplying LHS and simplifying 37*58*10^(a+b-2) = 2146*10^(c-4) => 2146 cancel's out both side and comparing powers of 10. a+b-2 = c - 4 => c = a + b + 2

Given (3.7 * (10^a) ) * (5.8 *(10^b)) = (0.2146 * (10^c)) we have to find c in terms of a and b. (3.7 * 5.8 ) * (10 ^(a+b)) = (0.2146 * (10^c)) (37*58 * (10^(-2)) * (10^(a+b)) = 2146 * (10^(-4)) * (10 ^c) NOTE : a^m * a^n = a^ (m+n) 2146 * 10^(a+b-2) = 2146 * 10^(c-4) cancel 2146 on both sides 10^(a+b-2) = 10^(c-4) as bases are equal, lets check exponents a+b -2 = c -4 a + b +2 = c Therefore, c = a + b + 2

the equation becomes 21.46*(10)^a+b = 21.46* (10)^c-2 equating the powers of 10 a+b = c-2 a+b+2=c is the answer

3.7*5.8=21.46=0.2146*10^{-2} Equation becomes: 0.2146*10^{-2}*10^a*10^b=0.2146*10^c Divide by 0.2146 to eliminate that, we end up with: 10^{-2}*10^a*10^b=10^c 10^{-2+a+b}=10^c We can take the base 10 out now and just deal with the exponents. Thus: a+b-2=c Answer is A!

Since all the values are multiplying, brackets may be removed. 3.7 x 5.8 x 10^a x 10^b = 0.2146 x 10^c 10^a x 10^b = 0.2146 x 10^c / 3.7 x 5.8 (taking 3.7 and 5.8 to RHS) 10^a x 10^b = 0.01 x 10^c (0.2146 divided by 3.7 and 5.8 gives 0.01) 0.01 can be written as 1/100 or 1/10^2 and then taking 10^2 to LHS 10^a x 10^b x 10^2 = 10^c Powers with the same base are added. Eg. 2^3 x 2^5 = 2^(3 + 5) = 2^8 Similarly, 10^(a+b+2) = 10^c Bases of both are 10. Hence, a+b+2 = c

0.37*10^(a+1)*0.58*10^(b+1) = 0.2146*10^c 0.2146*10^(a+1+b+1) = 0.2146*10^c c= a+b+2

B example 3.7 x 10^1 * 5.8 x 10 ^2 equals 20.05 x 10^3. 0.2146 needs to be multipled by 10^2 to get decimal in right place. there a must be added to b and add an addition 10^2 to get decimal correct.

Expanding the equation by multiplying 3.7x5.8= 21.46x10^a+bx10^2=0.2146x10^c Which can be be rewritten as 0.2146x10^a+b+2=0.2146x10^c Meaning c=a+b+c

convert fracts to whole => 37* (10 ^(a -1)) * (58 ^ (10^ (b-1)) = 2146 ^ (10^(c-4)) form the equation of powers a - 1 + b - 1 = c - 4 a+b -2 + 4 = c a+b+2 = c

In this type of problems, we should try to convert everything to the same base. Quickly enough we can see that is works when we multiply 3.7*5.8 = 21.46. Then we have 21.46*10^{a+b }= 21. 46 * 10^{c-2} (because 0.2146 = 21.46*10^{-2}) which becomes: a+b=c-2 or c=a+b+2