Solve each equation for the variable 96x27x18 4x310 lnx10lnx

Solve each equation for the variable:

9^6x=27^x+18

4^x-3=10

ln(x+10)+ln(x)=ln(x)

log(3x-10)-ln(x-2)=6

9^6x=27^x+18

3^12x=3^3x+54

^{12x = 3x+54}

^{9x = 54}

^{x =6}

4^x-3=10

(x-3) log4 = log10

x = 4.66

ln(x+10)+ln(x)=ln(x)

ln(x(x+10)) = ln(x)

x^2+10x = x

x^2+9x=0

x(x+9) = 0

x=0 or x = -9

here x=-9 not possible and also x=0 not possible

so,

there is no such x that satisfies this equation

log(3x-10)-ln(x-2)=6

(3x-1)/(x-2) = 10^6

3x-1 = 10^6x - 2*10^6

x = 2.000005