Find the value of \(m\) which satisfies \(\left(\frac{19}{10}\right)^7 \times \left(\frac{10}{19}\right)^6 \times \left(\frac{19}{10}\right)^{10} = \left(\frac{10}{19}\right)^{6m + 18}\).
\(-\frac{29}{6}\)
Combine the powers of \(\frac{19}{10}\) on the LHS: \(\left(\frac{19}{10}\right)^7 \times \left(\frac{19}{10}\right)^{10} = \left(\frac{19}{10}\right)^{17}\).
Convert \(\left(\frac{10}{19}\right)^6\) to base \(\frac{19}{10}\): \(\left(\frac{10}{19}\right)^6 = \left(\frac{19}{10}\right)^{-6}\).
So the LHS becomes: \(\left(\frac{19}{10}\right)^{17-6} = \left(\frac{19}{10}\right)^{11}\).
Express LHS in terms of \(\frac{10}{19}\): \(\left(\frac{19}{10}\right)^{11} = \left(\frac{10}{19}\right)^{-11}\).
Equate with RHS: \(6m + 18 = -11\).
Solve: \(6m = -29 \Rightarrow m = -\frac{29}{6}\).
Hence, the value of \(m\) is \(-\frac{29}{6}\).
Similar Questions
- Given that $7^{0.07} = x$, $7^{0.07} = y$ and $x^z = y^3$, then the value of z is close to:
- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- If $\sqrt{45} + \sqrt{125} = 17.89$, then what will be the value of $\sqrt{180} + \sqrt{80}$?
(Give your answer to one decimal place.) - What is the value of $\frac{4+\sqrt{2}}{\sqrt{2}+1}$?
If $\sqrt{2916} = 54$ then what is the value of the following?
$\sqrt{29.16} + \sqrt{0.2916} + \sqrt{0.002916} + \sqrt{0.00002916}$
- Find the value of $95^{-17} \div 95^{9} \times 95^{-15}$.
- $(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11})$ is equal to:
- What is the value of $\sqrt{75} + \sqrt{147}$?
- Find $\sqrt{\frac{1521}{1849}}$
If $\frac{2\sqrt{2}+\sqrt{7}}{2\sqrt{2}-\sqrt{7}} = x + y\sqrt{14}$, find the value of y.
Important Questions from Surds and Indices
Find the cube root of 78402752
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
