Solve for z over the real numbers:
5^(z+1)/3 = 25^z
Take the natural logarithm of both sides and use the identities log(a b) = log(a)+log(b) and log(a^b) = b log(a):
log(5) (z+1)-log(3) = 2 log(5) z
Expand out terms of the left hand side:
log(5) z-log(3)+log(5) = 2 log(5) z
Subtract 2 z log(5)-log(3)+log(5) from both sides:
-(log(5) z) = log(3)-log(5)
Divide both sides by -log(5):
Answer: | z = 1-(log(3))/(log(5))=0.317393805......
+129845 I'm assuming this is :
5^[(z+1)/3] = 25^z if so, we can write
5^[ (z + 1) / 3 ] = (5^2)^z
5^[ (z + 1)/ 3 ] = 5^(2z) since the bases are the same, we can solve for the exponents
[ z + 1 ] / 3 = 2z multiply both sides by 3
z + 1 = 6z subtract z from both sides
1 = 5z divide both sides by 5
1/5 = z
