Consider the following equations:
Rewrite each side of the equation with a base of 2.
Hence, solve for x.
8^{x} = 4
16^{x} = \dfrac{1}{2}
\dfrac{1}{1024} = 4^x
\left(\sqrt{2}\right)^{x} = \sqrt[5]{32}
Solve the following exponential equations:
4^{x} = 4^{8}
3^{x} = 3^{\frac{2}{9}}
3^{x} = 27
7^{x} = 1
8^{x} = \dfrac{1}{8^{2}}
3^{y} = \dfrac{1}{27}
10^{x} = 0.01
3^{x} = 3^{6}
6^{x} = 6^{ - 3 }
6^{x} = 6^{\frac{4}{3}}
2^{x} = 64
9^{x} = 1
5^{x} = \dfrac{1}{5^{2}}
10^{x} = 0.0001
9^{y} = 81
Solve for x in the following equations:
9^{y} = 27
25^{y} = 125
3^{ 5 x - 10} = 1
25^{x + 1} = 125^{ 3 x - 4}
9^{x + 4} = 27^{x}
3^{ 4 x - 8} = 1
8^{x + 3} = 32^{ 2 x - 1}
30 \times 2^{x - 6} = 15
2^{x} \times 2^{x + 3} = 32
3^{x} \times 9^{x - k} = 27
a^{x + 1} = a^{3} \sqrt{a}
3^{x^{2} - 3 x} = 81
27 \left(2^{x}\right) = 6^{x}
24 \times 2^{x - 6} = 12
2^{x} \times 2^{x + 2} = 16
3^{x} \times 9^{x - k} = 9
Solve the following exponential equations:
5^{x} = \sqrt[3]{5}
30^{n} = \sqrt[3]{30}
5^{x} = \sqrt{5}
5^{x} = \sqrt[4]{5}
9^{x} = \sqrt[9]{9}
\left(\sqrt{7}\right)^{y} = 49
\left(\sqrt{6}\right)^{y} = 36
Solve the following exponential equations:
\left(\dfrac{5}{8}\right)^{x} = \left(\dfrac{5}{8}\right)^{9}
7 \left(4^{x}\right) = \dfrac{7}{4^{3}}
\dfrac{1}{3^{x - 3}} = \sqrt[3]{9}
\left(\dfrac{1}{9}\right)^{x + 5} = 81
\left(\dfrac{1}{8}\right)^{x - 3} = 16^{ 4 x - 3}
\dfrac{25^{y}}{5^{4 - y}} = \sqrt{125}
8^{x + 5} = \dfrac{1}{32 \sqrt{2}}
\left(\dfrac{1}{25}\right)^{x - 4} = 125^{ 3 x - 1}
8^{x + 4} = \dfrac{1}{32 \sqrt{2}}
\left(\dfrac{1}{27}\right)^{x - 5} = 81
\dfrac{1}{5^{x + 3}} = \sqrt[3]{25}
9 \left(8^{x}\right) = \dfrac{9}{8^{2}}