Property 9
In exponential expressions, the expressions which are to be added are performed within parenthesis and transformed into a multiplication, then solved.
Example
\(2^x+2^{x+1}=24\)
\(2^x+2^x\cdot2=24\)
\(2^x\cdot(1+2)=24\)
\(3\cdot2^x=24\)
\(2^x=8\)
\(2^x=2^3\)
\(\Rightarrow x=3\)
1.
\(3^x+3^x=18\)
\(\Rightarrow x=?\)
2.
\(3\cdot2^x+2^x=32\)
\(\Rightarrow x=?\)
3.
\(3\cdot5^x-5^x+2\cdot5^x=100\)
\(\Rightarrow x=?\)
4.
\(2^4+2^4+2^4+2^4=?\)
5.
\(4\cdot3^2+6\cdot3^2-3^2=?\)
6.
\(5^{x+1}+2\cdot5^x-3\cdot5^x=20\)
\(\Rightarrow x=?\)
7.
\(2^{x+2}-3\cdot2^x+2^{x+1}=48\)
\(\Rightarrow x=?\)
8.
\(3^x+\samefrac{4}{3^{-x}}=45\)
\(\Rightarrow x=?\)
9.
\(5^{x+1}-2\cdot5^x=75\)
\(\Rightarrow x=?\)
10.
\(6^{x+2}+2\cdot6^x-3\cdot6^{x+1}=20\)
\(\Rightarrow x=?\)
11.
\(3^{x+1}+3^{x+2}=36\)
\(\Rightarrow x=?\)
12.
\(\samefrac{3^{x+3}+54}{3^x+2}=?\)
13.
\(\samefrac{2^{x+1}-2^x}{2^{x-1}+2^x}=?\)
14.
\(\samefrac{2^x\cdot2^x\cdot2^x\cdot2^x}{2^x+2^x+2^x+2^x}=2\)
\(\Rightarrow x=?\)
15.
\(\samefrac{6^{68}+6^{69}+6^{70}}{6^{69}+6^{70}+6^{71}}=?\)