a) \(3^x=243=3^5\Leftrightarrow x=5\).

b) \(5^m=625\Leftrightarrow5^m=5^4\Leftrightarrow m=4\).

c) By  \(16^x.5^{2x}=16^x.25^x=\left(16.25\right)^x=400^x\), so the done equation equivalant to   

                                                          \(400^x=400^1\Leftrightarrow x=1\).

d) \(2^{2n+2}+2^{2n}=160\Leftrightarrow2^{2n}\left(2^2+1\right)=160\Leftrightarrow2^{2n}=2^5\Leftrightarrow2n=5\Leftrightarrow n=2,5.\)

a) 3x=243=35⇔x=5

.

b) 5m=625⇔5m=54⇔m=4

.

c) By  16x.52x=16x.25x=(16.25)x=400x

, so the done equation equivalant to   

                                                          400x=4001⇔x=1

.

d) 22n+2+22n=160⇔22n(22+1)=160⇔22n=25⇔2n=5⇔n=2,5.

b) $5^m=625\iff 5^m=5^4\iff m=4$.

c) By  ${16}^x{.5}^{2x}={16}^x{.25}^x={\left(16.25\right)}^x={400}^x$, so the done equation equivalant to   

                                                          ${400}^x={400}^1\iff x=1$.

d) $2^{2n+2}+2^{2n}=160\iff 2^{2n}\left(2^2+1\right)=160\iff 2^{2n}=2^5\iff 2n=5\iff n=2,5.$

 Selected by MathYou

(a) 3^x=243

And: 3⁵= 243

=>x=5

(b) 5^m=625

And: 5⁴=625

=>m=4