Question

solve for x: 7^2x+3 =2401 . show substitution of your solution to verify the equation. show steps. show work.

Answer 1

To solve the equation 7^(2x+3) = 2401, use logarithms to isolate x. Verify the solution by substituting it back into the original equation.

Step-by-step explanation:

To solve the equation 7^(2x+3) = 2401, we need to use logarithms. Taking the logarithm of both sides, we get log(7^(2x+3)) = log(2401). Using the logarithm rule log(a^b) = b * log(a), we can simplify the equation to (2x+3) * log(7) = log(2401). Now, dividing both sides by log(7), we have 2x+3 = log(2401)/log(7). Solving for x, we subtract 3 from both sides and divide by 2, giving us x = (log(2401)/log(7) - 3)/2.

To substitute this solution back into the equation and verify it, we plug in the value of x into the original equation: 7^(2((log(2401)/log(7) - 3)/2)+3) = 2401. Simplifying this expression should yield the same value as the right side of the equation.

Answer 2

X= 1/2

Step-by-step explanation:

7^2x+3 =2401

7^(2x+3 )=2401

7^(2x+3 )= 7^4

Taking away the base because its equal to 7

Then solving the power as an equation

2x+3= 4

2x= 4-3

2x= 1

X=1/2

Now substituting x into the equation to know if we are correct

7^(2x+3 )=2401

Where x= 1/2

7^(2*(1/2) +3)= 7^4

7^(1+3)= 7^4

7^4= 7^4

7^4= 2401