help fast please

[low blaze]

Zero?

[coral bronze]

yea and

i think there will be

more solutions

[tulip depot]

taking log both sides

log a+b= log ab

so log 260^x=log120^x

using log power rule

take out x

x log 260=x log 120

try doing the rest from here

or are you not supposed to use log

[tulip depot]

or am i wrong

yeah im wrong i think

[sinful valve]

0

[coral bronze]

ok it s 0 cause u can see it

but can be any other number too

[sinful valve]

I don't think so

the closest we come is -inf

20^x dominates all the other exponentials for positive x
8^x dominates all the other exponentials for negative x

[copper nimbus]

2^2x(5^x-2^x) = 15^x-13^x
let's use log_(2)
2x + 2xlog(5^x-2^x) = log(15^x-13^x)
2x=log((15^x -13^x)/5^x -2^x)
let's consider x is not zero
if x is positive
15^x - 13^x is always even
5^x - 2^x is always odd
therefore, x is not a positive integer
if x is negative, we will have a similar outcome, therefore, x is not an integer

not sure how to make it for any real number
also, not sure the log part is needed

also, plotting the graph seems like a solution. only 0 and -inf gives a solution (they tend to 0 at -inf)

[covert robin]

.solved