Problem: If 10m=b−10n\log _{10} m=b-\log _{10} nlog10m=b−log10n, then m=m=m=
Answer Choices:
A. bn\dfrac{b}{n}nb
B. bnb nbn
C. 10bn10^{b} n10bn
D. b−10nb-10^{n}b−10n
E. 10bn\dfrac{10^{b}}{n}n10b Solution:
b=10m+10n=10mn;∴mn=10b;∴m=10b/nb=\log _{10} m+\log _{10} n=\log _{10} m n ; \quad \therefore m n=10^{b} ; \quad \therefore m=10 ^b / nb=log10m+log10n=log10mn;∴mn=10b;∴m=10b/n;
or
10m=1010b−10n=10(10b/n);∴m=10b/n\log _{10} m=\log _{10} 10^{b}-\log _{10} n=\log _{10}\left(10^{b} / n\right) ; \quad \therefore m=10^{b} / nlog10m=log1010b−log10n=log10(10b/n);∴m=10b/n.