exponential & logarithmic

1. Solve the equation e^(x) - 4 + 4e^(-x) = 0

Let y = e^x

e^(x) - 4 + 4e^(-x) = 0

y - 4 + 4/y = 0

y² - 4y + 4 = 0

(y - 2)² = 0

y = 2

e^x = 2

x = ln(2)


2. Solve the equation log(x²) = (log x)²

log(x²) = (log x)²

2*log(x) = (log x)²

(log x)² - 2(log x) = 0

(log x)(log x - 2) = 0

log x = 0 or log x = 2

x = 10⁰ or x = 10²

x = 1 or x = 100