Đáp án: 3.$x=16$
6.$x =15$
9.$x=110$
12.$x=15$
18.$x=20$
21.$x=33$
24.$x=15$
Giải thích các bước giải:
3.Ta có:
$8^x=16^{12}$
$\to \left(2^3\right)^x=\left(2^4\right)^{12}$
$\to 2^{3x}=2^{4\cdot 12}$
$\to 2^{3x}=2^{48}$
$\to 3x=48$
$\to x=16$
6.Ta có:
$8^x=32^9$
$\to \left(2^3\right)^x=\left(2^5\right)^9$
$\to 2^{3x}=2^{45}$
$\to 3x=45$
$\to x =15$
9.Ta có:
$8^x=32^{66}$
$\to \left(2^3\right)^x=\left(2^5\right)^{66}$
$\to 2^{3x}=2^{5\cdot 66}$
$\to 2^{3x}=330$
$\to 3x=330$
$\to x=110$
12.Ta có:
$16^x=64^{10}$
$\to \left(4^2\right)^x=\left(4^3\right)^{10}$
$\to 4^{2x}=4^{30}$
$\to 2x=30$
$\to x=15$
15.Ta có:
$\left(\dfrac18\right)^x=\left(\dfrac14\right)^6$
$\to \left(\left(\dfrac12\right)^3\right)^x=\left(\left(\dfrac12\right)^2\right)^6$
$\to \left(\dfrac12\right)^{3x}=\left(\dfrac12\right)^{12}$
$\to 3x=12$
$\to x =4$
18.Ta có:
$\left(\dfrac{1}{16}\right)^x=\left(\dfrac1{32}\right)^{16}$
$\to \dfrac{1}{16^x}=\dfrac{1}{32^{16}}$
$\to 16^x=32^{16}$
$\to \left(2^4\right)^x=\left(2^5\right)^{16}$
$\to 2^{4x}=2^{80}$
$\to 4x=80$
$\to x=20$
21.Ta có:
$\left(\dfrac19\right)^x=\left(\dfrac{1}{27}\right)^{22}$
$\to \dfrac1{9^x}=\dfrac1{27^{22}}$
$\to 9^x=27^{22}$
$\to \left(3^2\right)^x=\left(3^3\right)^{22}$
$\to 3^{2x}=3^{66}$
$\to 2x=66$
$\to x=33$
24.Ta có:
$\left(\dfrac49\right)^x=\left(\dfrac8{27}\right)^{10}$
$\to \left(\left(\dfrac23\right)^2\right)^x=\left(\left(\dfrac2{3}\right)^3\right)^{10}$
$\to \left(\dfrac23\right)^{2x}=\left(\dfrac23\right)^{30}$
$\to 2x=30$
$\to x=15$
