## burhan101 2 years ago Solve for x

1. burhan101

$\huge (5)(8)^{(x+2)} = 5^{7x}$

2. Hero

$5 \dot\ 8^{x+2} = 5^{7x} \\ 5 \dot\ 8^x 8^2 = \left(5{^7}\right)^x \\5 \dot\ 8^2 = \frac{\left(5{^7}\right)^x}{8^x} \\5 \dot\ 64 = \left(\frac{5^7}{8}\right)^x \\320 = \left(\frac{5^7}{8}\right)^x$ Take logs of both sides and finish simplifying

3. burhan101

|dw:1359086666173:dw|

4. burhan101

this is what i'm getting, but it is wrong

5. burhan101

wait, we're we sipposed to take the log of both sides?

6. Hero

$\ln(320) = \ln\left(\left(\frac{5^7}{8}\right)^x\right) \\\ln(320) = x \ln\left(\frac{5^7}{8}\right) \\\frac{\ln(320)}{\ln\left(\frac{5^7}{8}\right)} = x \\\frac{\ln(320)}{\ln5^7 - \ln2^3} = x \\\frac{\ln(320)}{7\ln5 - 3\ln2} = x$

7. Hero

Uh, ya....logs of both sides. What you do to one side, you do to the other side.

8. Hero

The last two lines, either form, is what you want.

9. burhan101

okay thanks !

10. Hero

By the way, don't forget that you are isolating x bro. Don't confuse the numerator and the denominator.

11. burhan101

yeah i know but im getting a weird answer idk why -.-

12. Hero

You should have gotten what I got above. And if you're approximating, you should get x ≈ 0.628

13. burhan101

14. Hero

You did not isolate x properly bro.

15. Hero

Take a look at your second to last step.

16. burhan101

ohhh, i figured it. i flipped it

17. burhan101

got it ! thanks man :)

18. Hero

Wow....bro