Question

If $\frac{{\log }_{10}a}{12}=\frac{{\log }_{10}b}{21}=\frac{{\log }_{10}c}{15},$ then $bc$ is equal to

• A. $a$
• B. $a^2$
• C. $a^3$
• D. $a^4$

Answer 1

The correct option is C $a^3$

Let $\frac{{\log }_{10}a}{12}=\frac{{\log }_{10}b}{21}=\frac{{\log }_{10}c}{15}=k$
Then, $a={10}^{12k},b={10}^{21k},c={10}^{15k}$
$\therefore bc={10}^{36k}=({10}^{12k}{)}^3=a^3$