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