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A study of urban density shows that the population density
C (in persons
//km^(2) ) is related to the distance a (in
km ) from the city centre by
log_(e)C=log_(e)z-va+ta^(4), where
z,v, and
t are positive constants. Solve for
C as a function of a.

A study of urban density shows that the population density $\mathrm{C}$ (in persons $/ \mathrm{km}^{2}$ ) is related to the distance a (in $\mathrm{km}$ ) from the city centre by $\log _{e} \mathrm{C}=\log _{e} \mathrm{z}-\mathrm{va}+\mathrm{ta}^{4}$ , where $\mathrm{z}, \mathrm{v}$ , and $\mathrm{t}$ are positive constants. Solve for $\mathrm{C}$ as a function of a.

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Write equations of sine and cosine functions using properties

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Q. A study of urban density shows that the population density

\mathrm{C}

(in persons

/ \mathrm{km}^{2}

) is related to the distance a (in

\mathrm{km}

) from the city centre by

\log _{e} \mathrm{C}=\log _{e} \mathrm{z}-\mathrm{va}+\mathrm{ta}^{4}

, where

\mathrm{z}, \mathrm{v}

, and

\mathrm{t}

are positive constants. Solve for

\mathrm{C}

as a function of a.

Write Equation: Write down the given logarithmic equation. $\newline$ The given equation is $\log_e(C) = \log_e(z) - va + ta^4$ , where $z$ , $v$ , and $t$ are positive constants.
Combine Terms: Use the properties of logarithms to combine the terms on the right side of the equation. $\newline$ Since $\log_e(z) - v_a + t a^4$ is written as a single logarithm, we can combine the terms using the properties of logarithms. However, we notice that the terms $v_a$ and $t a^4$ are not inside a logarithm, which indicates a potential issue with the equation as it stands. We need to correct this before proceeding.

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