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IrinaVladis [17]
3 years ago
5

Which equation has x = –6 as the solution?

Mathematics
2 answers:
olya-2409 [2.1K]3 years ago
3 0

Answer:

The equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. \log _3\left(-2x-3\right)=2  has x = –6 as the solution.

Step-by-step explanation:

<u>Checking the equation</u>

log Subscript 3 Baseline (negative 2 x minus 3) = 2

Writing in algebraic expression

\log _3\left(-2x-3\right)=2

Use the logarithmic definition

\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c

\log _3\left(-2x-3\right)=2\quad \Rightarrow \quad \:-2x-3=3^2

-2x-3=3^2

-2x-3=9

-2x=12

\mathrm{Divide\:both\:sides\:by\:}-2

\frac{-2x}{-2}=\frac{12}{-2}

x=-6

Therefore, the equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. \log _3\left(-2x-3\right)=2  has x = –6 as the solution.

KonstantinChe [14]3 years ago
3 0

Answer:

(-2x-3)=2

Step-by-step explanation:

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For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)


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g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2


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SECOND.

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g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2


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g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1


As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.


<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

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