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In the system of equations, $c$ is a constant. For which values of $c$ does the system have no solution?

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Identify properties of logarithms

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Q. In the system of equations,

c

is a constant. For which values of

c

does the system have no solution?

Identify Equations: Identify the system of equations. Let's assume the system is: $\newline$ $ax + by = c$ $\newline$ $dx + ey = f$ $\newline$ where $a, b, c, d, e,$ and $f$ are constants, and $k$ is involved in one of these constants.
No Solution Condition: Determine the condition for no solution. A system of linear equations has no solution if the lines are parallel. This happens when the ratios of the coefficients of $x$ and $y$ are equal, but the constant terms are not proportional: $\newline$ $\frac{a}{d} = \frac{b}{e} \neq \frac{c}{f}$
Assume Coefficient Involvement: Assume $k$ affects one of the coefficients. Let's say $k$ is part of $e$ , so $e = k$ . Then the condition becomes: $\newline$ $\frac{b}{k} = \frac{a}{d}$ $\newline$ Solving for $k$ , we get: $\newline$ $k = \frac{b \cdot d}{a}$

More problems from Identify properties of logarithms

Question

Write the exponential equation in logarithmic form.

\newline

9^3 = 729

\newline

\log_\square 729 = 3

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Write the exponential equation in logarithmic form.

\newline

e^4 \approx 54.598

\newline

\ln\_\_\_\_ \approx 4

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Write the logarithmic equation in exponential form.

\newline

\log_{10}100 = 2

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10^2 = \underline{\hspace{2em}}

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Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

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\frac{\ln (e)}{10} =

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Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

\newline

\log_3 33 =

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Evaluate. Round your answer to the nearest thousandth.

\newline

\log_{5}50 =

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Question

Which property of logarithms does this equation demonstrate?

\newline

\log_3 3 + \log_3 6 = \log_3 18

\newline

\newline

\text{Product Property}

\newline

\text{Power Property}

\newline

\text{Quotient Property}

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Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log(uv)

\newline

Posted 3 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log v^7

\newline

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Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of base-

6

logarithms or multiples of base-

6

logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log_6 w^6

\newline

Posted 3 months ago