Solve the Equation: 2ln(x)−ln (7x)=1

This is an equation laid out in terms of the natural logarithm, which essentially is the reverse function of e^x . From this equation we need to find a solution for x =? Since we know that this equation involves logarithms, we should keep the logarithm laws in mind, which are;
e^ln(x)= xln(a) + ln(b) = ln(ab)aln(b) = ln(a^b)
1) Firstly we should change the first term of the equation, using the logarithm laws 3rd logarithm law from above, so that 2ln(x) = ln(x²) 2) Combine all the terms on the left hand side of the equation to form one term, using the 2nd log law to give you : ln(x²/7x) = 13) Now we can undo the natural logarithm to give us an equation in terms of x, using the 1st log law stated above. Therefore x²/7x = e¹4) We can now rearrange this equation and factorise it to find solutions of x:x²=e7x (by multiplying across by 7x)x²-7ex=0 (subtracting 7ex from both sides)x(x-7e)=0 (factorising)Therefore --> x=0 or x =7e