5^(x+5) < 5^5

[KK]

While solving for x, 5^(x+5) = 5^5. we simply proceed with x+5=5, can we do the same in case of <=, >= or <, > signs in the equation.

thanks

[RonPurewal]

While solving for x, 5^(x+5) = 5^5. we simply proceed with x+5=5, can we do the same in case of <=, >= or <, > signs in the equation.

thanks

in this equation, yes.
in ANY equation, not necessarily.

here's why:
exponentials, as long as their bases are greater than 1, are strictly increasing functions. this means that if A is greater than B, then 5^A must also be greater than 5^B. therefore, because of this property (called "monotonicity" if you're a math geek), you can trust that the inequality works the same way for the exponentials as for the numbers in the exponents.
(notice that with bases less than 1, it's the exact opposite: if A is larger than B, for instance, 0.8^A is smaller than 0.8^B. therefore, in that case, you would turn all the "greater than"s into "less than"s, and vice versa.)

if you're dealing with OTHER functions, especially functions that get smaller, turn around, and then get bigger again (such as quadratic functions), then you can't do this. for instance, if x^2 > 4, then this means that x could be > 2 but also x could be < -2.

hth!