How would I simplify the sum of the following logarithm: log(4*100)?

log(4*100) = log 4 + log 100 I think you have got this bit.

Now we use the definition of a logarithm . Since we are dealing with logs to the base 10 we have:

(1) log to base 10 of 100 = x, hence by definition 10^x = 100. So we can see that x = 2 since
10^2 = 100.

(2) log to base 10 of 4 = y, hence by definition 10^y = 4. So we can see that it is not obvious what the value of y is and we cannot evaluate y without using a calculator. So log 4 cannot be simplified.

Hence we finally have:

log (4*100) = log 4 + 2

one law of logarithms is this:

log (a • b) = log a + log b

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log (4 • 100)

= log 4 + log 100
= log 4 + 2 ---> final answer!

1.) (e^-3 * e^4)/(e^-2 * e^-1) Use the rule: Powers of terms with the same base add up when multiplied and subtracted when divided 2.)e^lnx e^lnx =Y Take natural log on both sides and proceed 3.)e^3lnx e^3lnx =Y Take natural log on both sides and proceed lne^3lnx=lnY 3lnx=lnY rules of logs lnx³=lnY which gives x³=Y For the following proceed as above 4.)5e^(1/2lnx) 5.)6lne 6.)4lne+lne 7.)lne^4 8.)lne^lnx

log(4 * 100)
= log(4) + log(100)
= log(4) + log(10^2)
= log(4) + 2 (≈ 2.60205999)

log (4 • 100) = log 4 + log 100 = log 4 + 2

log(4 * 100) = 2.60205999

100 log 4 = 100 in log base 4