+1904 Solve for x. Please show how you got to your answer.
\(\frac{{2x}^{2}}{\sqrt{{x}^{4}}}+2=\frac{5}{\sqrt{{3}^{x}}}\)
+23246 Solve: 2x2 / sqrt( x4 ) + 2 = 5 / sqrt( 3x )
Since sqrt( x4 ) = x2 ---> 2x2 / sqrt( x4 ) ---> 2x2 / x2 ---> 2
Therefore: 2x2 / sqrt( x4 ) + 2 = 2 + 2 = 4
The problem reduces to: 4 = 5 / sqrt( 3x )
Multiply both sides by sqrt( 3x ) to get 4·sqrt( 3x ) = 5
Square both sides: 16 · 3x = 25
---> 3x = 25 / 16
Find the log of both sides: log( 3x ) = log( 25 / 16)
---> x · log( 3) = log( 25 / 16 )
---> x = log( 25 / 16) / log( 3 )
---> x = 0,406228 (approximately)
+23246 Solve: 2x2 / sqrt( x4 ) + 2 = 5 / sqrt( 3x )
Since sqrt( x4 ) = x2 ---> 2x2 / sqrt( x4 ) ---> 2x2 / x2 ---> 2
Therefore: 2x2 / sqrt( x4 ) + 2 = 2 + 2 = 4
The problem reduces to: 4 = 5 / sqrt( 3x )
Multiply both sides by sqrt( 3x ) to get 4·sqrt( 3x ) = 5
Square both sides: 16 · 3x = 25
---> 3x = 25 / 16
Find the log of both sides: log( 3x ) = log( 25 / 16)
---> x · log( 3) = log( 25 / 16 )
---> x = log( 25 / 16) / log( 3 )
---> x = 0,406228 (approximately)
+1904 After you find a possible solution, it would be a good idea to plug the possible solution into the origional equation to see if the possible solution is a solution which I will do now.
\(\frac{{2(0.406228)}^{2}}{\sqrt{{0.406228}^{4}}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(\frac{2(0.165021187984)}{\sqrt{{0.406228}^{4}}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(\frac{0.330042375968}{\sqrt{{0.406228}^{4}}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(\frac{0.330042375968}{\sqrt{0.0272319924836507}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(\frac{0.330042375968}{0.1650211879840001031}+2=\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(1.9999999999999987504635 +2=\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(3.9999999999999987504635 =\frac{5}{\sqrt{{3}^{0.406228}}}\)
\(3.9999999999999987504635 =\frac{5}{\sqrt{1.5624999533947653}}\)
\(3.9999999999999987504635 =\frac{5}{1.249999981357905981}\)
\(3.9999999999999987504635 = 4.000000059654701750471\)
\(3.9999999999999987504635 ≠ 4.000000059654701750471\)
Because only one possible solution was found and it turned out not to be a solution, there is no solution.
