Question

Find the exponential Inequality

5^(2x + 2 )< 625

Answer 1

to solve this, you first take the natural log of both sides
\[\ln(5^{2*x+2})<\ln(625)\]
Using laws of logarithms,
\[(2x+2)*\ln(5)<\ln(625)\]
solving for x
\[x<({\ln(625)/\ln(5)}-2)/2\]

Answer 2

\[5^{2x+2}\leq 5^4\iff 2x+2\leq 4\]
no need for logs

Answer 3

\[2x+2\leq 4\]
\[2x\leq 2\]
\[x\leq 1\]

Answer 4

the only thing you need to know for this problem is that \(5^4=625\)