Exponential Equation - Let’s solve the equation using logarithms

How to use logarithms to solve an exponential equation.

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TC Math Notes

[joseeoliviero]

Don't need to use log, in this case, if you know your "rules of power". 3^2x+1 = 81. Change 81 to 3^4. (rule - if a^b=a^c; b=c). Therefore, 2x+1=4. 2x=3, x=3/2 or 1.5.

[robertgamble]

I viewed your solution and when I solved it I didn’t distribute the log3 into (2x + 1). I got the same answer and it was easier:
Thank you for all the great teachings.
Math Problems
➖➖➖➖➖➖➖
3^(2x + 1) + 5 = 86
3^(2x + 1) = 81
log3^(2x + 1) = log81
(2x + 1)log3 = log81
(2x + 1) = log81/log3
(2x + 1) = 4
2x = 3
x = 3/2
➖➖➖➖➖➖➖➖

[guyreece]

I like your step wise method of solving. Thanks for your efforts.

[deograciousuwiragiye]

86-5=81
81=3 power 4
Now can equalize
2x+1=4
2x =3
X =2/3
If I make proof by replacing x by its value, the equation is correct.

[billrandle]

The equation can be rewritten
3^(2x+1) = 86 - 5
i. e. 3^(2x+1)=81
Now 81 =3^4

Equating exponents gives us
2x+1=4 that is x = 3/2

[yusrnm]

This one is easy to solve without logarithms. It's easy to see that (2x+1) = 4), So 2x=3 and X=1.5 (exactly, not approximately).

[kennethwright]

2x+1 obviously equals 4, since 3^4=81, so x =3/2

[russophilej]

3 raised to what power is 81 ??? Set
exponent equal to 4 ... it worked this
time ... but not the "general case" ...
Logs are the better way !!! Be well ...

[mracjesstark]

No need to use log..where 81=3⁴

2X+1-4=0
2x-3=0
2x=3
X=3/2
X=1.5

[johnplong]

No calculators back in my Day just tables in the back of the book I did this using the rules of exponents ( power rule)1.5

[aryusure]

I got it but most certainly not with the right method.
But common sense still works since it's easy to see that 3 to the power 2x + 1 = 81 (86 minus 5).
Once you get that you notice that 81 = 3 to the 4th power (3 X 3 X 3 X 3 = 81).
So 2x + 1 must equal 4.
So 2x = 3 (4 minus 1)
Bingo! X = 1.5

[olivemd]

I got the correct answer, but your explanation confused me.
Edit: I will listen a few more times. Maybe I should ask my son if he can give me an old scientific calculator. I’m from the ancient times( before calculators).

[grahamwatts]

solve the equation using logarithms - I'm not sure people get the point of the question here i.e. use logs!

[jjfishingproductions]

Just get to the point man you talk to much just get to the point it’s wasting time and it’s annoying

[homepropsllc]

Why do u confuse us with all these logs, f(x), lns, sins, cos, etc.
I got migraine just looking and listening to ur method.
I solved within 12 seconds as follows:
PROBLM.

3^(2x+1) + 5 = 86
SOLTN.
3^(2x+1) = 86 - 5
3^(2x+1) = 81
3^(2x+1) = 3⁴
Therefore, 2x+1= 4
2x=4-1
2x=3
x =3/2 =1.5 Ans.

[rossbatrossbdotcom]

He kept saying the answer is approximately 1.50 when it is in fact, exactly 1.50