If log 2=x, log 3=y and log 7=z, then the val | vedclass

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

Question

(B) Given: $\log 2=x, \log 3=y, \log 7=z$.We need to find the value of $\log (4 \sqrt[3]{63})$.$\log (4 \sqrt[3]{63}) = \log (2^2 \cdot (3^2 \cdot 7)^

Vedclass · Accepted Answer

$2 x+\frac{2}{3} y+\frac{1}{3} z$

Vedclass · Answer

(B) Given: $\log 2=x, \log 3=y, \log 7=z$.We need to find the value of $\log (4 \sqrt[3]{63})$.$\log (4 \sqrt[3]{63}) = \log (2^2 \cdot (3^2 \cdot 7)^{1/3})$Using the logarithmic properties $\log (ab) = \log a + \log b$ and $\log (a^n) = n \log a$:$\log (4 \sqrt[3]{63}) = \log (2^2) + \log ((3^2 \cdot 7)^{1/3})$$= 2 \log 2 + \frac{1}{3} \log (3^2 \cdot 7)$$= 2 \log 2 + \frac{1}{3} (\log 3^2 + \log 7)$$= 2 \log 2 + \frac{1}{3} (2 \log 3 + \log 7)$Substituting the given values:$= 2x + \frac{1}{3} (2y + z)$$= 2x + \frac{2}{3} y + \frac{1}{3} z$.

If $\log 2=x, \log 3=y$ and $\log 7=z,$ then the value of $\log (4 \sqrt[3]{63})$ is

Similar Questions

If $\log _{10} 2986 = 3.4751$,then $\log _{10} 0.02986 =$

If $\log _{a}(a b)=x,$ then $\log _{b}(a b)$ is

$\frac{3+\log _{10} 343}{2+\frac{1}{2} \log _{10} \left(\frac{49}{4}\right)+\frac{1}{3} \log _{10} \left(\frac{1}{125}\right)}=$

If $0 < a < 1$,$0 < x < 1$,and $x < a$,then $\log_{a} x$ is:

$7 \log \frac{16}{15} + 5 \log \frac{25}{24} + 3 \log \frac{81}{80} =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module