Answer :
Answer:
n = 4.6477
Step-by-step explanation:
We can solve the exponential equation using logarithm by using these rules:
[tex]\boxed{a^c=b\Longleftrightarrow log_ab=c}[/tex] ... [1]
[tex]\boxed{log_a(b\times c)=log_ab+log_ac }[/tex]... [2]
[tex]\boxed{log_aa=1}[/tex] ... [3]
[tex]\boxed{log_ab=\frac{log_cb}{log_ca} }[/tex] ... [4]
Therefore, for
[tex]12^{n-3}=60[/tex]
[tex]log_{12}(60)=n-3[/tex] (applying the [1] rule)
[tex]log_{12}(12\times5)=n-3[/tex]
[tex]log_{12}(12)+log_{12}(5)=n-3[/tex] (applying the [2] rule)
[tex]1+log_{12}(5)=n-3[/tex] (applying the [3] rule)
[tex]n=log_{12}(5)+4[/tex]
[tex]\displaystyle n=\frac{log_{10}(5)}{log_{10}(12)}+4[/tex] (applying the [4] rule)
by using the calculator or logarithm table, we can find out:
[tex]n=0.6477+4[/tex]
[tex]\bf n=4.6477[/tex]
