nmomma83
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A logarithm is just another way to write an exponent!
Exponential Form
3²=9
4³ = 64
27 = 128
+ 100%
Logarithmic Form
log
log
||

au 1 A logarithm is just another way to write an exponent Exponential Form 39 4 64 27 128 100 Logarithmic Form log log class=

Respuesta :

Answer:

see explanation

Step-by-step explanation:

A property of logarithms is

• [tex]log_{b}[/tex] x = n ⇒ x ⇔ [tex]b^{n}[/tex]

Then

3² = 9 ← in exponential form , is

[tex]log_{3}[/tex] 9 = 2 ← in logarithmic form

---------------------------------

4³ = 64 ← in exponential form , is

[tex]log_{4}[/tex] 64 = 3 ← in logarithmic form

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[tex]2^{7}[/tex] = 128 ← in exponential form , is

[tex]log_{2}[/tex] 128 = 7 ← in logarithmic form

semsee45

Answer:

[tex]3^2=9 \implies \boxed{\log_{3}9=2}[/tex]

[tex]4^3=64 \implies \boxed{\log_{4}64=3}[/tex]

[tex]2^7=128 \implies \boxed{\log_{2}128=7}[/tex]

Step-by-step explanation:

To write the given exponential equations in logarithmic form, we can use the following rule:

[tex]\boxed{\begin{array}{c}\underline{\textsf{Logarithmic Rule}}\\\\a^c=b \iff \log_ab=c\end{array}}[/tex]

For the exponential equation 3² = 9:

  • a = 3
  • b = 9
  • c = 2

Therefore, the logarithmic form is:

[tex]\Large\boxed{\boxed{\log_{3}9=2}}[/tex]

For the exponential equation 4³ = 64:

  • a = 4
  • b = 64
  • c = 3

Therefore, the logarithmic form is:

[tex]\Large\boxed{\boxed{\log_{4}64=3}}[/tex]

For the exponential equation 2⁷ = 128:

  • a = 2
  • b = 128
  • c = 7

Therefore, the logarithmic form is:

[tex]\Large\boxed{\boxed{\log_{2}128=7}}[/tex]

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