0. Functions

Logarithmic Functions

0. Functions

Logarithmic Functions

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Multiple Choice

Convert the following exponential expression to its equivalent logarithmic form.
$e^9=x+3$

$\log\left(x+3\right)=9$

$\ln\left(x+3\right)=9$

$\ln9=x+3$

$\log_9x=e^3$

Verified step by step guidance

Identify the given exponential expression: e^9 = x + 3.

Recall the relationship between exponential and logarithmic forms: If a^b = c, then log_a(c) = b.

Apply this relationship to the given expression: e^9 = x + 3 can be rewritten in logarithmic form as ln(x + 3) = 9.

Understand that ln represents the natural logarithm, which is the logarithm with base e.

Verify the conversion by checking that the logarithmic form ln(x + 3) = 9 correctly represents the original exponential expression e^9 = x + 3.

7:3m

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Textbook Question

ln x is unbounded Use the following argument to show that lim (x → ∞) ln x = ∞ and lim (x → 0⁺) ln x = −∞.

c. Show that ln 2ⁿ > n/2 and ln 2^(−n) < −n/2.

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Multiple Choice

Convert the following logarithmic expression to its equivalent exponential form.

$\log_4x=5$

Convert the following logarithmic expression to its equivalent exponential form.

$x=\log9$

Convert the following exponential expression to its equivalent logarithmic form.

$3^{x}=7$

{Use of Tech} Let f(x) = ln((x+1)/(x-1)) and g(x) = ln ((x+1)/(x-1)).

b. Sketch graphs of f and g to show that these functions do not differ by a constant.

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Textbook Question

Convert the following expressions to the indicated base.

$2 to the x-th power$ using base e

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Textbook Question

Solving equations Solve the following equations.

log₈ x = 1/3

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Textbook Question

Find the inverse $f^{-1}\left(x\right)$ of each function (on the given interval, if specified).

$f\left(x\right)=e^{2x+6}$

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Logarithmic Functions practice set

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Struggling with Calculus?

Convert the following exponential expression to its equivalent logarithmic form.e9=x+3e^9=x+3e9=x+3

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Logarithmic Functions practice set

Convert the following exponential expression to its equivalent logarithmic form.
$e^9=x+3$