# Homework solving exponential equation, logarithmic equation and exponential equation.

I need help with three homework questions.¨

First one:

$$\sqrt{3x^2-2x-15}=x+1$$ I don't know how to get the right answer. The answer is supposed to be 4. I get: $$3x^2-2x-15=(x+1)^2$$ $$3x^2-2x-15=x^2+2x+1$$ $$2x^2-4x-14=0$$ $$x^2-2x-7=0$$

$$x_1=1+\sqrt8$$ $$x_2=1-\sqrt8$$

Second question is: $$ln(x-7)-2ln(x-1)=-2ln5$$ where i come to this stage but don't know how to solve it $$\frac{x-7}{(x-1)^2}=\frac{1}{25}$$

the answer is supposed to be $x=11$ or $x=16$

Third question is $$9^x-4*3^x+3=0$$

I have come this far $$3^{2x}-4*3^x+3=0$$

answer is supposed to be $x=1$ or $x=0$

• 1st question: when you went from $-15$ to $-14$ you should have gone to $-16$ instead. – vadim123 Oct 28 '15 at 22:46
• Welcome to the site! In the future, please separate your questions into different posts. – Théophile Oct 28 '15 at 23:01

1) $-15 - 1 = -16$ not $-14$.
2) multiply by sides to get: $25(x -7) = (x - 1)^2$
3) $3^{2x} + 4*3^x + 3 = 0$. Let $y = 3^x$ so to get $y^2 + 4y + 3 = 0$. Easier?
• I understand question 1) and 3) now thank you. on question 2 I dont't understand how that helps me? shall I change forms to $$25x-175=x^2-2x+1$$? I don't understand how that makes it easier. – Fredrik Nyberg Oct 28 '15 at 23:14
• You just need to solve for x, don't you? $25(x−7)=(x−1)^2 \implies 25x−175=x^2−2x+1 \implies x^2 - 27x + 176 = 0$ (if I didn't make any mistakes which I probably did.--- no, i didn't) – fleablood Oct 29 '15 at 0:04