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Karolina [17]
3 years ago
12

Simplify the expression below and write it as a single logarithm:

Mathematics
2 answers:
BabaBlast [244]3 years ago
5 0

Answer:

log((x+4)^3)x-7)^2 / (x-2)^5 x^2)

Step-by-step explanation:

OLEGan [10]3 years ago
4 0

The simplification of 3log(x + 4) – 2log(x – 7) + 5log(x - 2) - log(x^2) is \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)

<u>Solution:</u>

Given, expression is 3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)

We have to write in as single logarithm by simplifying it.

Now, take the given expression.

\rightarrow 3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)

Rearranging the terms we get,

\left.\rightarrow 3 \log (x+4)+5 \log (x-2)-2 \log (x-7)+\log \left(x^{2}\right)\right)

\text { since a } \times \log b=\log \left(b^{a}\right)

\rightarrow \log (x+4)^{3}+\log (x-2)^{5}-\left(\log (x-7)^{2}+\log \left(x^{2}\right)\right)

\text { We know that } \log a \times \log b=\log a b

\rightarrow \log \left((x+4)^{3} \times(x-2)^{5}\right)-\left(\log \left((x-7)^{2} \times\left(x^{2}\right)\right)\right.

\text { We know that } \log a-\log b=\log \frac{a}{b}

\rightarrow \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)

Hence, the simplified form \rightarrow \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)

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