Question

Solve for n. 25^n−3=5^n+8 Enter your answer in the box.

Answer 1

`25^n-3=5^n+8`

`(5^n)^2-3=5^n+8`, by recognising 25 = 5²

`(5^n)^2-5^n-11=0`

`y^2-y-11=0`, by letting
`y=5^n`

`y= (-1 \pm √((-1)^2-(4*1*-11)))/(2*1) = (1 \pm 3√(5))/(2)`, using the quadratic formula

`y=5^n= (1 + 3\sqrt5)/(2)`.

`n = \log_5( (1+3√(5))/(2) )`, note you could simplify this further using log laws if you are familiar with these.

Notice that
`(1-3√(5))/(2) \ \textless \ 0` so this is not a solution as logarithms are only defined for positive values of x.

Answer 2

The answer is N=14

Glad to help ^w^