Exponential Equations

[giddyupc]

Solve the equation:

(ax)^ln(a)=(bx)^ln(b)
ln(ax)^ln(a)=ln(bx)^ln(b)

ln(a) X ln(ax)=ln(b) X ln(bx)

ln(a)²+(lna X lnx) =ln(b)²+(lnb X lnx)

(lna X lnx)-(lnb X lnx)=ln(b)²+ln(a)²

lna(lnx)-lnb(lnx)=ln(b)²+ln(a)²

lna-lnb(lnx)=ln(b)²+ln(a)²

lnx=[ln(b)²+ln(a)²] / [lna-lnb]

x=e^{[ln(b)2+ln(a)2] / [lna-lnb]}


I attempted to solve this equation, but I'm honestly not sure about my work. Could someone tell me if I have made a mistake somewhere?

 

[Deleted member 4993]

Solve the equation:

(ax)^ln(a)=(bx)^ln(b)

a^ln(a) * x^ln(a) = b^ln(b) * x^ln(b)

[x^ln(a)]/[x^ln(b)] = [b^ln(b)]/[a^ln(a)]

x^{[ln(a)-ln(b)]} = [b^ln(b)]/[a^ln(a)]

Now finish it.......

ln(ax)^ln(a)=ln(bx)^ln(b)

ln(a) X ln(ax)=ln(b) X ln(bx)

ln(a)²+(lna X lnx) =ln(b)²+(lnb X lnx)

(lna X lnx)-(lnb X lnx)=ln(b)²+ln(a)²

lna(lnx)-lnb(lnx)=ln(b)²+ln(a)²

lna-lnb(lnx)=ln(b)²+ln(a)²

lnx=[ln(b)²+ln(a)²] / [lna-lnb]

x=e^{[ln(b)2+ln(a)2] / [lna-lnb]}


I attempted to solve this equation, but I'm honestly not sure about my work. Could someone tell me if I have made a mistake somewhere?

.