Question

if log 16/81=x(log2-log3)then find value of2x-1​

Answer 1

(2x - 1) = 7

Step-by-step explanation:

Given that $\log \frac{16}{81} = x(\log 2 - \log 3)$ and we have to find the value of (2x - 1).

Now, given

$\log \frac{16}{81} = x(\log 2 - \log 3)$

⇒ $\log(\frac{2}{3})^{4} = x \log \frac{2}{3}$

{Since we know the logarithmic property as $\log A - \log B = \log \frac{A}{B}$ }

⇒ $4 \log \frac{2}{3} = x \log \frac{2}{3}$

{Since, we know the logarithmic property as $\log x^{a} = a \log x$ }

⇒ x = 4 {Cancelling the log part from both sides}

Therefore, (2x - 1) = 2 × 4 - 1 = 7 (Answer)