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Conditions on the Domain and the Range of the Logarithmic Function

If 25 = 32, t...

Question

If $2^{5} = 32$ , then in logarithmic form, it can be written as

A

2

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B

5

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C

32

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Solution

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5^{4} = 625

can be written in logarithmic form as .

how is it written in logarithmic form

log 5 - 1

can be written as a single logarithm with base as

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2 log 2 - 3 log 4

can be written as a single logarithm with base as

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Limits that lead to the indeterminate forms

1^{\infty}, 0^{0}, \infty^{0}

can sometimes be solved taking logarithm first and then using L' Hospital's rule

lim x \to a (f (x))^{g (x)}

is in the form of

\infty^{0}

, it can be written as

e^{{lim}_{x \to a} g (x) ln f (x)} = e^{L}

L = lim x \to a \frac{ln f (x)}{\frac{1}{g (x)}}

\frac{\infty}{\infty}

form and can be solved using L' Hopital's rule.

lim x \to 0^{+} (s i n x)^{2 s i n x}

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Conditions on the Domain and the Range of the Logarithmic Function

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