Question

[Trần Năng Nhân]

Tìm a;b

b) 2^a + 342 = 7^b
c) 2^a + 80 = 3^b
d) 5^a + 9999 = 20b
e) 10^a + 168 = b^2
f) 5^a + 323 = b^2

Answer 1

[HT.Phong (9A5)]

b) Ta có:

\(7^b=2^a+342\) 

\(\Rightarrow\left\{{}\begin{matrix}7^b=343\\2^a=7^b-342\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}7^b=7^3\\2^a=343-342\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}b=3\\2^a=2^0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}b=3\\a=0\end{matrix}\right.\) 

c) Ta có:

\(2^a+80=3^b\)

\(\Rightarrow\left\{{}\begin{matrix}3^b=81\\2^a=3^b-80\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}3^b=3^4\\2^a=81-80\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}b=4\\2^a=2^0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}b=4\\a=0\end{matrix}\right.\)

d) Ta có:

\(5^a+9999=20b\)

\(\Rightarrow\left\{{}\begin{matrix}5^a=1\\20b=9999+5^a\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}5^a=5^0\\20b=9999+1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=0\\b=\dfrac{10000}{20}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=0\\b=500\end{matrix}\right.\)

e) \(10^a+168=b^2\)

\(\Rightarrow\left\{{}\begin{matrix}10^a=1\\b^2=168+10^a\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}10^a=10^0\\b^2=168+1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=0\\b^2=169\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=0\\\left[{}\begin{matrix}b=13\\b=-13\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left(a;b\right)=\left(0;13\right);\left(0;-13\right)\) 

f) \(5^a+323=b^2\)

\(\Rightarrow\left\{{}\begin{matrix}5^a=1\\b^2=5^a+323\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}5^a=5^0\\b^2=324\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=0\\b^2=18^2\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=0\\\left[{}\begin{matrix}b=18\\b=-18\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left(a;b\right)=\left(0;18\right);\left(0;-18\right)\)

Answer 2

[Jackson Williams]

b) a = 0

    b = 3

c) a = 0

    b = 4

d) a = 0 

    b = 500

e) a = 0

    b ∈ {13; -13}

f) a = 0

   b ∈ {18; -18}