Question

how many real solutions are there to the equation 5^6x+3 *25^3x+6= 125^4x+5

Answer 1

is this the equation?\[5^{6x}+3\cdot 25^{3x}+6=125^{4x}+5\]

Answer 2

no the +6 and +5 are in the exponents too

Answer 3

ok:\[5^{6x}+3\cdot 25^{3x+6}=125^{4x+5}\]first write everything as powers of 5:\[5^{6x}+3\cdot (5^2)^{3x+6}=(5^3)^{4x+5}\]\[\iff 5^{6x}+3\cdot 5^{6x+12}=5^{12x+15}\]

Answer 4

okay what next?

Answer 5

i think has only one real solution -1.000453818549