Question

Answer 1

a) \(2^x=4^7\Rightarrow2^x=\left(2^2\right)^7\Rightarrow2^x=2^{14}\Rightarrow x=14\)

b) \(3^x=81^2\Rightarrow3^x=\left(3^4\right)^2\Rightarrow3^x=3^8\Rightarrow x=8\)

c) \(5^x=125^4\Rightarrow5^x=\left(5^3\right)^4\Rightarrow5^x=5^{12}\Rightarrow x=12\)

d) \(7^x=49^5\Rightarrow7^x=\left(7^2\right)^5\Rightarrow7^x=7^{10}\Rightarrow x=10\)

e) \(4^x=8^7\Rightarrow\left(2^2\right)^x=\left(2^3\right)^7\Rightarrow2^{2x}=2^{21}\Rightarrow2x=21\Rightarrow x=\dfrac{21}{2}\notin Z\left(loại\right)\Rightarrow x\in\varnothing\)

f) \(8^x=16^4\Rightarrow\left(2^3\right)^x=\left(2^4\right)^4\Rightarrow2^{3x}=2^{16}\Rightarrow3x=16\Rightarrow x=\dfrac{16}{3}\notin Z\left(loại\right)\Rightarrow x\in\varnothing\)