Solve for x by using log. Rounded to hundredth. [tex]10^{4x-5}=e^{3x}[/tex]

Answer: [tex]x=1.85[/tex]Step-by-step explanation:  Given the expression [tex]10^{4x-5}=e^{3x}[/tex], apply natural logarithm to both sides. Then: [tex]ln(10)^{4x-5}=ln(e)^{3x}[/tex] Remember that according the the properties of logarithms: [tex]ln(a)^m=mln(a)[/tex] [tex]ln(e)=1[/tex] Then: [tex](4x-5)ln(10)={3x}[/tex] Apply distributive property and solve for "x". Then you get: [tex]4x*ln(10)-5ln(10)=3x\\\\4x*ln(10)-3x=5ln(10)\\\\x(4ln(10)-3)=5ln(10)\\\\x=\frac{5ln(10)}{4ln(10)-3}\\\\x=1.85[/tex]