Question

25^(x2)(5^(7x))=625

Answer 1

what about it?

Answer 2

i have to solve the exponential equation... the solutions.

Answer 3

25 squared is equal to 625. That means (x2)(5^(7x)) = 2

Answer 4

the question is asking you to find x... so that 5 to a poweris equal to 625

simplify the some terms with 5 as the base



25 = 5^2 and 625 = 5^4

then

\[(5^2)^{x^2} \times (5)^{7x} = 5^4\]

simplify using the power laws

\[5^{2x^2} \times5^{7x} = 5^4\]

when multiplying add the powers

\[5^{2x^2 + 7x} = 5^4\]

equate the powers and solve for x

\[2x^2 + 7x = 4\]

or

\[2x^2 + 7x - 4= 0\]

solve the quadratic

(2x -1)(x+4)=0

x = 1/2 or -4

then with value of x, found above, will result in 625 when substituted into the original equation