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Convert each of the following to exponential form and solve
a. n= log_(4) 16384
b. 6= log_(b) 46656
(i need someone to solve this for me emergency



Answer :

Answer:

(a)

[tex]\texttt{the exponential form}:\bf 4^n=16384\\\texttt{the solution}:\bf n=7[/tex]

(b)

[tex]\texttt{the exponential form}:\bf b^6=46656\\\texttt{the solution}:\bf b=6[/tex]

Step-by-step explanation:

To find the exponential form for [tex]n=log_4(16384)[/tex] and [tex]6=log_b(46656)[/tex], we apply this principle:

[tex]\boxed{log_a(b)=c\ \Longleftrightarrow\ a^c=b}[/tex]

where:

  • [tex]a=\texttt{base}[/tex]
  • [tex]b=\texttt{argument}[/tex]
  • [tex]c=\texttt{exponent}[/tex]

(a)

[tex]n=log_4(16384)[/tex]

given:

  • [tex]\texttt{base (a)}=4[/tex]
  • [tex]\texttt{argument (b)}=16384[/tex]
  • [tex]\texttt{exponent (c)}=n[/tex]

Now we can find its exponential form:

[tex]a^c=b[/tex]

[tex]\bf 4^n=16384[/tex]

Next, we can find the solution:

[tex]4^n=16384[/tex]

[tex]4^n=4^7[/tex]

[tex]\bf n=7[/tex]

(b)

[tex]6=log_b(46656)[/tex]

given:

  • [tex]\texttt{base (a)}=b[/tex]
  • [tex]\texttt{argument (b)}=46656[/tex]
  • [tex]\texttt{exponent (c)}=6[/tex]

Now we can find its exponential form:

[tex]a^c=b[/tex]

[tex]\bf b^6=46656[/tex]

Next, we can find the solution:

[tex]b^6=46656[/tex]

[tex]b^6=6^6[/tex]

[tex]\bf b=6[/tex]

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