We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
32
1
avatar

Solve the equation 9^(5-x)=1/(sqrt(15^(4x)). Express your answer in terms of ln3 and ln5.

 Nov 28, 2019
 #1
avatar+23542 
+1

Solve the equation \(9^{5-x}= \dfrac{1}{\sqrt{15^{4x}}}\).

Express your answer in terms of \(\ln3\) and \(\ln5\) .

 

\(\begin{array}{|rcll|} \hline 9^{5-x} &=& \dfrac{1}{\sqrt{15^{4x}}} \\ 9^{5-x} &=& \dfrac{1}{15^{\frac{4x}{2}}} \\ 9^{5-x} &=& \dfrac{1}{15^{2x}} \\ 9^59^{-x} &=& \dfrac{1}{15^{2x}} \\ 9^53^{-2x} &=& \dfrac{1}{15^{2x}} \\ 9^5 &=& \dfrac{3^{2x}}{15^{2x}} \\ 9^5 &=& \left(\dfrac{3}{15}\right)^{2x} \\ 9^5 &=& \left(\dfrac{1}{5}\right)^{2x} \\ 9^5 &=& \dfrac{1}{5^{2x}} \\ 9^55^{2x} &=& 1 \\ 3^{2\cdot 5}5^{2x} &=& 1 \\ 3^{10}5^{2x} &=& 1 \\ 5^{2x} &=& 3^{-10} \quad | \quad \ln \text{ both sides } \\ 2x\ln(5) &=& -10\ln(3) \quad | \quad : 2 \\ x\ln(5) &=& -5\ln(3) \quad | \quad : 2 \\\\ \mathbf{x} &=& \mathbf{ -\dfrac{5\ln(3)}{\ln(5)} } \\ \hline \end{array}\)

 

laugh

 Nov 29, 2019

36 Online Users

avatar
avatar