Question

7^(x-2)=12^x

Answer 1

Take log on both sides!

Answer 2

\[\ln7^{x-2}=\ln12^x\]\[(x-2)\ln7=xln12\]
continued

Answer 3

\[x \ln7-2\ln7=x \ln12\]\[x \ln7-\ln49-x \ln12=0\]\[x(\ln7-\ln12)=\ln49\]now you have two choices for exact answer

Answer 4

Wait so what are they?

Answer 5

The answers? it equals ln 49?

Answer 6

\[x=\frac{\ln49}{\ln7-\ln12}\]or\[x=\frac{\ln49}{\ln \left( \frac{7}{12} \right)}\]

Answer 7

does that equal a decimal?

Answer 8

yes you have to use a calculator
\[x \approx -7.22\]

Answer 9

Oh, okay. so I would just plug that in to my calculator??? Thank you so much

Answer 10

welcome