11. Assuming you are trying to solve for xx, start by taking the logarithm of both sides.
a^x=10^(2x+1)ax=102x+1
log(a^x)=log(10^(2x+1))log(ax)=log(102x+1)
22. Using the logarithmic property, log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)logb(mn)=n⋅logb(m), simplify the equation.
xlog(a)=(2x+1)log(10)xlog(a)=(2x+1)log(10)
33. Expand the brackets.
xlog(a)=2xlog(10)+log(10)xlog(a)=2xlog(10)+log(10)
44. Move all terms with xx to one side of the equation with the terms with no xx to the other side.
2xlog(10)-xlog(a)=-log(10)2xlog(10)−xlog(a)=−log(10)
55. Factor out xx.
x(2log(10)-log(a))=-log(10)x(2log(10)−log(a))=−log(10)
66. Isolate for xx.
color(green)(|bar(ul(color(white)(a/a)x=(-log(10))/(2log(10)-log(a))color(white)(a/a)|)))
