SOLUTION: I do believe this is an exponential equation. Not sure how to solve using the calculator TI-84 or by hand. Your help would be appreciated. Thank you. TJ
5*6^4x+3-15=20
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Question 312696: I do believe this is an exponential equation. Not sure how to solve using the calculator TI-84 or by hand. Your help would be appreciated. Thank you. TJ
5*6^4x+3-15=20 the ^ represents the exponent 4x+3 above the 6
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'm presuming you mean:
Add 15 to both sides and divide both sides by 5:
Take the log of both sides -- but to which base? Actually, in the final analysis, it doesn't matter. The only thing that could possibly influence your decision would be if you have a calculator that can find the log to ANY valid base. I don't know if the TI-84 will do that or not. MS Excel will do it if you know how. Assuming that you only have ln and log (base 10) available, pick one and proceed:
\ =\ \ln(7))
Use:
\ =\ n\log_b(x))
\ln\left(6\right)\ =\ \ln(7))
Divide by )
\ =\ \frac{\ln(7)}{\ln(6)})
Add -3 and divide by 4:
}{\ln(6)}\ -\ 3}{4})
Is the exact answer -- use your calculator for a numeric approximation.
Now if you actually have the ability to take the log to any base, you can take the base 6 log, thus:
\ =\ \log_6(7))
\log_6\left(6\right)\ =\ \log_6(7))
But \ =\ 1)
, so:
\ =\ \log_6(7))
\ -\ 3}{4})
A somewhat simpler calculation.
John
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