An Exponential Log Equation

[@francorota8638]

I like that what matters the most in this channel is the way you get to the answer, rather than the answer itself.

[@BukhalovAV]

For log based 10 usually is used lg. For natural log - ln. Don't know, why English speakers mathematicians don't use this designation, but in Russian school we always use lg for 10, ln for e and log for other bases, and we don't have problems with discrepancies.

[@SidneiMV]

x^(log3) + x^(log5) = 8 x = 10^u 10^(ulog3) + 10^(ulog5) = 8 3^u + 5^u = 8 => u = 1 => *x = 10*

[@mtaur4113]

I have gotten too used to log being used for base e. In some situations it's the accepted convention. I'm not sure whether it's a Newton's Method or if you could rig up a Lambert W if the numbers were less convenient, such as if the RHS were 9.

[@Nothingx303]

I solved it using my foot 😊 by just interchanging the logarithmic argument with the Exponential base after that I compared which one of my leg smells better 😅 then I got 10 as the final answer Caution:- Don't try this at school 😊

[@YT_Admin_]

I could see the answer (10) in just one second but your solution is satisfying

[@SweetSorrow777]

Yup, I see it, too.

[@rakenzarnsworld2]

3+5=8 x = 10

[@scottleung9587]

I got x=10 right away.

[@Fire_Axus]

it is (hroot^log_3(5)(8))^(1/log3)

[@Fire_Axus]

spoiler: there are no other complex solutions

[@glumbortango7182]

That's assuming you're restricted to the range (0,2π) for the angle, there's infinitely many solutions otherwise (one of them is roughly 25.3023 * e^(9.7167i) for example)