Einstein Failed To Solve This | An IMPOSSIBLE Exponential Equation

[@rogierownage]

This is the hardest clickbait i've seen in a while. None of this is very advanced at all

[@PotentialDevGcimOgism.]

The only problem i can find here is that the limit of 5^x - 7^(x+1) only gets to zero if we slide in the negative side. Tried it in desmos and got that x is likely equal to -5.78

[@elsupremoclash7419]

-5,78

[@pedrosso0]

What do you mean Impossible? You jusr solved it.

[@vladivascanu108]

with todays tools. back them it was way more difficult

[@aetheriox463]

i used a different method:
5^x = 7^(x+1)
ln(5^x)=ln(7^(x+1))
xln(5)=(x+1)ln(7)
x/(x+1)=ln(7)/ln(5)
from here, i used the change of base formula, but backwards:
log_e(7)/log_e(5)=log_5(7)
So
x/(x+1)=log_5(7)
x=(log_5(7))(x+1)
x=xlog_5(7)+log_5(7)
x-xlog_5(7)=log_5(7)
x(1-log_5(7))=log_5(7)
x = (log_5(7))/(1-log_5(7))
this is the same as your answer, but i find it fun that i was able to come up to a different method to find the same solution :]

[@deliberatelyaverage]

You, unintentionally, helped me learn the change of base method for my final. Thank you internet stranger

[@aetheriox463]

@@deliberatelyaverage it works with any base, not just e :]

[@elsupremoclash7419]

@@aetheriox463 even easier, if 7^(x+1) then: 7•7^x

[@cosfor5154]

there is no solutions because graphs of y = 5^x and y = 7^(x+1) do not intersect

[@KristofferBrander]

They do on the negative side at x≈5.78.