Questions: Use the definition of a logarithmic function to write the exponential equation as an equation involving a single logarithm 4^2=16 The equivalent equation involving a single logarithm is (Type an equation. Do not simplify.)

Use the definition of a logarithmic function to write the exponential equation as an equation involving a single logarithm 4^2=16 The equivalent equation involving a single logarithm is (Type an equation. Do not simplify.)
Transcript text: Use the definition of a logarithmic function to write the exponential equation as an equation involving a single logarithm \[ 4^{2}=16 \] The equivalent equation involving a single logarithm is $\square$ (Type an equation. Do not simplify.)
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Exponential Equation

The given exponential equation is

42=16 4^{2} = 16

Step 2: Convert to Logarithmic Form

To convert the exponential equation to logarithmic form, we identify the base, exponent, and result:

  • Base: 44
  • Exponent: 22
  • Result: 1616

Using the definition of a logarithm, we can express the equation as:

log⁡4(16)=2 \log_{4}(16) = 2

Final Answer

The equivalent equation involving a single logarithm is

log⁡4(16)=2 \boxed{\log_{4}(16) = 2}

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
During the mid-1770s, political dissent was stimulated by the printing and circulation of short books called pamphlets, pulp novels, paperbacks, POD books
failedAnswered
Are the ratios 2:3 and 3:4 equivalent?
failedAnswered
What led many Americans to call for a stronger central government and revise/replace the Articles of Confederation? Bacon's Rebellion Land Ordinance of 1785 Northwest Ordinance of 1785 Shays' Rebellion
failedAnswered
Use the given graph to estimate the value of each derivative. (i) (a) f'(0) (b) f'(1) (c) f'(2) (d) f'(3) (e) f'(4) (f) f'(5)
failedAnswered
An arctic ecologist measures the thickness of an ice floe. The thickness is 0.343 m. What is the thickness in centimeters? Write your answer as decimal.