## burhan101 Group Title Solve for x one year ago one year ago

1. burhan101 Group Title

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

2. Hero Group Title

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

3. burhan101 Group Title

|dw:1359086666173:dw|

4. burhan101 Group Title

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

5. burhan101 Group Title

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

6. Hero Group Title

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

7. Hero Group Title

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

8. Hero Group Title

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

9. burhan101 Group Title

okay thanks !

10. Hero Group Title

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

11. burhan101 Group Title

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

12. Hero Group Title

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

13. burhan101 Group Title

14. Hero Group Title

You did not isolate x properly bro.

15. Hero Group Title

Take a look at your second to last step.

16. burhan101 Group Title

ohhh, i figured it. i flipped it

17. burhan101 Group Title

got it ! thanks man :)

18. Hero Group Title

Wow....bro