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Sagot :
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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