Without actually calculating the logarithm, determine what two integers the value of log(1.37×109) falls between.

First we need to find out what kind of logarithm rule is given, the given is logarithm product rule which states that a log of a product is equal to the sum of the log of the first base and the log of the second base.

By:

= log (1.37 x 10⁹) = log (1.37) + log (10⁹)

= log (1.37) + 9

= 9 + log (1.37)

In the meantime, 1.37 is between 1 and 10 its logarithm will be between 0 and 1. Thus, the value of log (1.37 x 10⁹) falls between 9 and 10 because when you compose a scientific notation you will always have a number among 1 and 10 by 10 to some power. That power tells you the integer part of the logarithm.

i believe the correct answer is b.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116