If log (2 a-3 b)=log a-log b, then a= | vedclass

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

Question

(A) Given the equation: $\log (2 a-3 b)=\log a-\log b$Using the logarithmic property $\log x - \log y = \log (x/y)$,we get:$\log (2 a-3 b)=\log (a/b)$

Vedclass · Accepted Answer

$\frac{3 b^{2}}{2 b-1}$

Vedclass · Answer

(A) Given the equation: $\log (2 a-3 b)=\log a-\log b$Using the logarithmic property $\log x - \log y = \log (x/y)$,we get:$\log (2 a-3 b)=\log (a/b)$By taking the antilog on both sides,we have:$2 a-3 b = a/b$Multiply both sides by $b$:$2 a b - 3 b^{2} = a$Rearrange the terms to isolate $a$:$2 a b - a = 3 b^{2}$$a(2 b-1) = 3 b^{2}$Therefore,$a = \frac{3 b^{2}}{2 b-1}$

If $\log (2 a-3 b)=\log a-\log b,$ then $a=$

Similar Questions

If $\log _{10} 50+\log _{10} 20=x,$ then $x$ is equal to

The value of $\log _{2} 16$ is

If $a^{2}+b^{2}=c^{2},$ then $\frac{1}{\log _{c+a} b}+\frac{1}{\log _{c-a} b}=$

If $3+\log _{5} x=2 \log _{25} y,$ then $x=$

If $(4.2)^{x} = (0.42)^{y} = 100$,then $\frac{1}{x} - \frac{1}{y} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module