Melody

Good try guest answerer but

ln(x) + ln(4x) = 2

\(ln(x) + ln(4x) = 2\\ e^{ln(x) + ln(4x) }=e^ 2\\ e^{ln(x) } \textcolor{red}{\times }e^{ ln(4x) }=e^ 2\\ x \textcolor{red}{\times }4x=e^ 2\\ 4x^2=e^ 2\\ etc\)

7x - 1 = 2x + 5

subtract 2x from both sides

then

add 1 to both sides

then you decide what to do.   :)

log4x+log5(x-6)=2

\(x\approx 8.179\)

Here is a graphical solution

x^2=27

\(x^2=27\\ x=\pm\sqrt{27}\\ x=\pm\sqrt{9*3}\\ x=\pm\sqrt{9}\sqrt{3}\\ x=\pm3\sqrt{3}\\\)

What system?

X marks the spot  - on a treasure map.   :)

How do I distribute the x on the outside to the numbers in the parentheses?

x(x+5)(x+5) 

\(x(x+5)(x+5) \\ x\times (x+5)(x+5) =x\times(x^2+10x+25)=x^3+10x^2+25x\\ or\\ x(x+5)\times (x+5)=(x^2+5x)(x+5)=x^3+5x^2+5x^2+25x=x^3+10x^2+25x\)

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You have good manners too.  That is excellent :))