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Alex Ar [27]
4 years ago
11

2log(x-3)+1=5 can someone explain how to solve for x?

Mathematics
1 answer:
Brums [2.3K]4 years ago
5 0
\bf 2log(x-3)+1=5\iff 2log_{10}(x-3)+1=5\\\\\\ 2log_{10}(x-3)=4
\\\\\\
log_{10}(x-3)=\cfrac{4}{2}\implies log_{10}(x-3)=2\\\\
-----------------------------\\\\
{{  a}}^{log_{{  a}}x}=x\impliedby \textit{using this cancellation rule}\\\\
-----------------------------\\\\
10^{\cfrac{}{}log_{10}(x-3)}=10^2\implies x-3=10^2\implies x=100+3
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Answer:

The polynomial will be P(x) = - 5 (x + 2)²(x - 3)

Step-by-step explanation:

The degree of the polynomial P(x) is 3 and it has zeros at x = - 2 with multiplicity 2 and at x = 3 with multiplicity 1.

Therefore, (x + 2)² and (x - 3) are the factors of the equation.

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