anonymous
  • anonymous
Solve for x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\huge (5)(8)^{(x+2)} = 5^{7x}\]
Hero
  • 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
anonymous
  • anonymous
|dw:1359086666173:dw|

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anonymous
  • anonymous
this is what i'm getting, but it is wrong
anonymous
  • anonymous
wait, we're we sipposed to take the log of both sides?
Hero
  • Hero
\[\ln(320) = \ln\left(\left(\frac{5^7}{8}\right)^x\right) \\\ln(320) = x \ln\left(\frac{5^7}{8}\right) \\\frac{\ln(320)}{\ln\left(\frac{5^7}{8}\right)} = x \\\frac{\ln(320)}{\ln5^7 - \ln2^3} = x \\\frac{\ln(320)}{7\ln5 - 3\ln2} = x\]
Hero
  • Hero
Uh, ya....logs of both sides. What you do to one side, you do to the other side.
Hero
  • Hero
The last two lines, either form, is what you want.
anonymous
  • anonymous
okay thanks !
Hero
  • Hero
By the way, don't forget that you are isolating x bro. Don't confuse the numerator and the denominator.
anonymous
  • anonymous
yeah i know but im getting a weird answer idk why -.-
Hero
  • Hero
You should have gotten what I got above. And if you're approximating, you should get x ≈ 0.628
anonymous
  • anonymous
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Hero
  • Hero
You did not isolate x properly bro.
Hero
  • Hero
Take a look at your second to last step.
anonymous
  • anonymous
ohhh, i figured it. i flipped it
anonymous
  • anonymous
got it ! thanks man :)
Hero
  • Hero
Wow....bro

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