What is the correct option from given options? pls explain your answer

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2 Answers
Oct 13, 2017

Answer nº 2

1 + 2log_10 2

Explanation:

Let's start by putting 250 in the form of 25*10:

" " log_10 (25*10)

Using the multiplication property of logarithms (log_a (x*y) = log_a x + log_a y); and writing 25 as 5^2

" " log_10 (5^2*10) = log_10 10 + log_10 5^2

Knowing that log_a a = 1 (log_10 10 = 1), and the power property of logarithms (log_a x^n = n log_a x)

" "log_10 10 + log_10 5^2 = 1 + 2 log_10 5

Hope that helped!!

Oct 13, 2017

Option 3) 3-2log_(10) 2

Explanation:

There are a few ways to do this, but this is the method I used. It will use the following properties of logarithms:

log_a (b^c) = c*log_a b color(white)(aaaaaa)"Exponent Property"

log_a (b/c) = log_a b - log_a c color(white)(aaaaaa)"Quotient Property"

log_a a = 1 color(white)(aaaaaaa)"Identity Property"

Begin by recognizing that 250 = 1000/4, and rewrite the original logarithm:

log_10 250 = log_10 (1000/4)

Now apply the Quotient Property above to split this logarithm into two separate logarithms:

log_10 (1000/4) = log_10 1000 - log_10 4

Rewrite both logarithms using exponents:

log_10 1000 - log_10 4 = log_10 (10^3) - log_10 (2^2)

Apply the Exponent Property:

log_10 (10^3) - log_10 (2^2) = 3*log_10 10 - 2*log_10 2

Finally, apply the Identity Property:

3*log_10 10 - 2*log_10 2 = 3(1) - 2*log_10 2 = 3 - 2 log_10 2