# How to rearrange this equation

#### michaelsmith559

##### Well-known Member
How can I rearrange this equation to solve for C169 and how can it be rearranged to solve for EXP(1)?

\$B\$2*(EXP(1)^(C169*A169))=D169

Thanks for the help.

Mike

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Try:- EXP(1)=(D169/\$B\$2)^(1/(C169*A169)

EXP(1) is a constant. This gives you the relationship between the cells.

LN(D169)-LN(\$B\$2) = C169*A169

(EXP(1)^(C169*A169)) doesn't make a lot of sense to me. This is surely the same as just doing EXP(C169*A169)?
If so then to just re-write in general algebra we have (where e is Euler's number);

b*e^ca=d

To solve for c just use natural logs;
ln(be^ca)=ln(d)
ln(b)+ln(e^ca)=ln(d)
ln(b)+ca*ln(e)=ln(d)
ln(b)+ca=ln(d) (as ln(e) = 1)
ca=ln(d)-ln(b)
ca=ln(d/b)
c=(ln(d/b))/a

To "solve" for e is a bit weird. Perhaps do the same but take logs to base 10 instead so you still have an "e" when you "anti-log".

how can i rearrange this equation to solve for c169

=ln(d169 / \$b\$2) / a169

Works great. With this I can plug back in some values and see if I get Euler's number.

Let me ask this another way to clarify for myself. If I know \$B\$2, EXP(1) or 2.718281828, and A169 do I have to know D169 to solve for C169? Can I just use B2, Exp(1), and A169 to solve for C169?

No.

Your equation in D169 can be (should be) rewritten as

=\$B\$2*EXP(C169*A169)

D169 clearly depends on C169. Solving for C169 clearly depends on the value of D169.

Okay. Is it correct to assume that trying to solve for C169 without D169 would be like trying to solve one equation with two unknowns, which is impossible?

It's an equation in four variables. If you know any three, you can solve for the fourth.

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