Without using log, Solve for x.[tex]25^{2x+3} = 125^{x}[/tex]
Accepted Solution
A:
Answer:x = -6Step-by-step explanation:We recognize that 25 = 5^2 and also 125 = 5^3, thus we can write:[tex]25^{2x+3}=125^x\\(5^2)^{2x+3}=(5^3)^x[/tex]Now we can use the property of exponents [[tex](a^x)^y=a^{xy}[/tex]] to simplify it:[tex](5^2)^{2x+3}=(5^3)^x\\5^{2(2x+3)}=5^{3x}\\5^{4x+6}=5^{3x}[/tex]We equate the exponents (since we have similar base) to find the value of x:4x + 6 = 3x4x - 3x = -6x = -6