If log _{30} 3=a and log _{30} 5=b, then find | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given that $\log _{30} 3 = a$ and $\log _{30} 5 = b.$We know that $\log _{30} 15 = \log _{30} (3 	imes 5) = \log _{30} 3 + \log _{30} 5 = a + b.$

Vedclass · Accepted Answer

$3(1-a-b)$

Vedclass · Answer

(A) Given that $\log _{30} 3 = a$ and $\log _{30} 5 = b.$We know that $\log _{30} 15 = \log _{30} (3 	imes 5) = \log _{30} 3 + \log _{30} 5 = a + b.$Also,$\log _{30} 15 = \log _{30} \left(\frac{30}{2}ight) = \log _{30} 30 - \log _{30} 2 = 1 - \log _{30} 2.$Equating the two expressions for $\log _{30} 15$:$a + b = 1 - \log _{30} 2 \Rightarrow \log _{30} 2 = 1 - a - b.$Now,$\log _{30} 8 = \log _{30} (2^3) = 3 \log _{30} 2.$Substituting the value of $\log _{30} 2$:$\log _{30} 8 = 3(1 - a - b).$

If $\log _{30} 3=a$ and $\log _{30} 5=b,$ then find the value of $\log _{30} 8.$

Similar Questions

If $\log_{10} 2 = 0.3010$,the number of digits in $2^{64}$ is:

If $\log 2 = 0.3010$ and $\log 3 = 0.4771,$ then the value of $\log _{5} 512$ is

If $\log x = \frac{\log y}{2} = \frac{\log z}{5}$,then $x^{4} \cdot y^{3} \cdot z^{-2} = $

$2 \log _{10} 5 + \log _{10} 8 - \frac{1}{2} \log _{10} 4 = ?$

If $\frac{\log x}{b-c} = \frac{\log y}{c-a} = \frac{\log z}{a-b}$,then $xyz = x^a \cdot y^b \cdot z^c = x^{b+c} \cdot y^{c+a} \cdot z^{a+b} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module