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Nostrana [21]
3 years ago
12

What is the relationship between exponentials and logarithms? How can you use these to solve equations? Provide an example in yo

ur explanation.
Mathematics
1 answer:
Sveta_85 [38]3 years ago
4 0

Answer:

Exponentials and logarithms are inverses of each other.

Step-by-step explanation:

Exponentials and logarithms are inverses of each other.

For logarithmic function:

Domain = \left ( 0,\infty  \right ), Range = \left ( -\infty ,\infty  \right )

Vertical asymptote is y - axis.

x - intercept is (1,0)

For exponential function:

Domain = \left ( -\infty ,\infty  \right ), Range = \left ( 0,\infty  \right )

Horizontal asymptote is x - axis.

y- intercept is (0,1)

Both exponential and logarithmic functions are increasing.

For example:

Solve: \log x=\frac{\log 5+\log 3}{\log 3^2}

\log x=\frac{\log 5+\log 3}{\log 3^2}\\\log x=\frac{\log (5\times 3)}{2\log 3}\,\,\left \{ \because \log (ab)=\log a+\log b\,,\,\log a^b=b\log a \right \}\\=\frac{\log 15}{2\log 3}

\Rightarrow \log x=\frac{\log 15}{2\log 3}\\\Rightarrow x=e^{\frac{\log 15}{2\log 3}}\,\,\left \{ \because \log x=y\Rightarrow x=e^y \right \}

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Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the la
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