Math Is Fun Forum

DAN7891

Guest

Cubic Logarithms

Can anyone help me solve this please:

27^x-3^(x+1)-3=0

Thanks in advance

Ps. it should be 0.68 but i dont know how to work it out

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Cubic Logarithms

Maybe I'm missing something, but I don't see how to get there analytically. The -3 messes stuff up.
You can get as close to the answer as you need to with a numerical method though.

Put a starting number into your calculator (say, 1).
Then do "log(3^(Ans+1)+3)÷(3log3)" and press equals lots of times until you're bored.

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Why did the vector cross the road?
It wanted to be normal.

sce1912

Member

Registered: 2008-10-08

Posts: 5

Re: Cubic Logarithms

Hi DAN7891,

Do you need an exact solution or just an approximation?

An approximation can be achieved quite easily with trial and improvement

To get an exact answer you need to solve a cubic equation in 3^x this can be done(as cubics go the equation is relatively easy to solve)

I can post further details of how to solve the equation to get an exact answer if that is what's required.