First of all, let us start by doing simple changes:
19+2lnx=252lnx=25−92nx=6----------------------->>>>> we applied simple side by side manipulations, now we will do the division by 2 in both the sides, it will end up this:
lnx=3--------------->>>>>> now we will use the inverse of ln, which is eelnx=e3x=e3 ----->>> now you should use a calculator or the problem may have this as solution depending on the assignment guidelines.
The approximate solution of this equation is equivalent to [tex]20.09[/tex].
What is logarithms?
For [tex]$x > 0$[/tex] and [tex]$b > 0$[/tex], $b\ne 1$, [tex]$y={{\log }_{b}}x$[/tex] is equivalent to [tex]${{b}^{y}}$[/tex] is equal to [tex]$x$[/tex].
The function [tex]$f\left( x \right)$[/tex] is equal to [tex]${{\log }_{b}}x$[/tex] is the logarithmic function with base [tex]$b$[/tex].
The given equation is,
[tex]$19+2\ln x=25$[/tex]
Subtract [tex]19[/tex] from both sides.
[tex]$19+2\ln \left( x \right)-19=25-19$[/tex]
Simplify it.
[tex]$2\ln \left( x \right)=6$[/tex]
Divide both sides by [tex]$2$[/tex].
[tex]$\frac{2\ln \left( x \right)}{2}=\frac{6}{2}$[/tex]
Simplify it.
[tex]$\therefore \ln \left( x \right)=3$[/tex]
Apply log rules [tex]$\log ab=N$[/tex] , [tex]${{a}^{N}}$[/tex] is equal to [tex]$b$[/tex].
[tex]$\therefore x={{e}^{3}}$[/tex]
The value of [tex]$e\approx 2.718$[/tex].
[tex]$x\approx {{\left( 2.718 \right)}^{3}}$[/tex]
[tex]$x\approx 20.09$[/tex]
Hence, the solution is equivalent to [tex]20.09[/tex].
Learn more about logarithmic function here,
https://brainly.com/question/3181916
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