Question

a)4^{2x - 6} = 1

b)2^x-1= 16

c)5<5^x<125

d)5^x+1= 125

e)5^2x-3 - 2. 5² = 5^{2 . 3}

Answer 1

\(a,4^{2x-6}=1\)\(\Leftrightarrow2x-6=0\Leftrightarrow2x=6\Rightarrow x=3\)

\(b,2^{2x-1}=16\Rightarrow2^{2x-1}=2^4\)

\(\Rightarrow2x-1=4\Rightarrow2x=5\Rightarrow x=\frac{5}{2}\)

\(c,5< 5^x< 125\Rightarrow5^1< 5^x< 5^3\)\(\Rightarrow1< x< 3\)

\(d,5^{x+1}=125\Rightarrow5^{x+1}=5^3\Rightarrow x+1=3\Rightarrow x=2\)

Answer 2

\(a,4^{2x-6}=1\)

\(4^{2x-6}=4^0\)

\(\Rightarrow2x-6=0\)

\(\Rightarrow2x=6\Leftrightarrow x=3\)

\(b,2^{x-1}=16\)

\(2^{x-1}=2^4\)

\(\Rightarrow x-1=4\)

\(\Rightarrow x=5\)

Answer 3

a)4^2x-6=1=>4^2x-6=1=4^0   b)2^x-1=16=2^4  c) 5=5^1<5^x<125=5^3  d)5^x+1=125=5^3 

=>2x-6=0=>2x=6=>x=3             =>x-1=4=>x=5    =>x=2                            => x+1=3=>x=2

e)=>5^2x-3-50=75

=>5^2x-3=25=5^2

=>2x-3=2

=>2x=5=>x=5/2