Đáp án:
a) `x=3`.
b) `x=0`.
c) $\begin{array}{l}a)\ S=\dfrac{5^{2007}-5}{4}\\b)\ x=2007\end{array}$
Giải thích các bước giải:
a) `3^(x-1)=9`
`=>3^(x-1)=3^2`
`=>x-1=2`
`=>x=3`
Vậy `x=3`.
b) `(x+2)^5-2^2. 3=20`
`=>(x+2)^5-12=20`
`=>(x+2)^5=32`
`=>(x+2)^5=2^5`
`=>x+2=2`
`=>x=0`
Vậy `x=0`.
c)
+) a) `S=5+5^2+5^3+...+5^2006`
`=>5S=5.(5+5^2+5^3+...+5^2006)`
`=>5S=5^2+5^3+5^4+...+5^2007`
`=>5S-S=(5^2+5^3+5^4+...+5^2007)-(5+5^2+5^3+...+5^2006)`
`=>4S=5^2007-5`
`=>S=(5^2007-5)/4`
+) b) `4S+5=5^x`
`=>4*(5^2007-5)/4+5=5^x`
`=>5^2007-5+5=5^x`
`=>5^2007=5^x`
`=>x=2007`
Vậy `x=2007`.
