6.03 Solving logarithmic equations
Solve for y in each of the following logarithmic equations:
\log_{10} y = 2
\log_{7} y = 5
\log_{\sqrt{49}} \left(y\right) = 3
\log_{y} 6 = \dfrac{1}{2}
\log_{y} \left(\sqrt{6}\right) = 3
\log_{2} y^{4} + \log_{2} y = 10
Solve for x in each of the following logarithmic equations:
\log_{16} x = \dfrac{1}{4}
\log_{25} x = \dfrac{3}{2}
\log_{4} \left( 5 x\right) = 3
2 \log x = 4
\dfrac{1}{2} \log_{7} x = \dfrac{5}{8}
\log_{6} \left( 3 x - 9\right) = 2
\log_{10} \left( 3 x + 982\right) = 3
\log_{9} \left( 7 x + 5\right) = 4
\log_{3} \left(6 - x\right) = \dfrac{1}{2}
6 \log_{4} \left( 2 x\right) - 18 = 0
\log_{7} \left(x^{3} - 15\right) = 2
\log_{2} \left(\log_{2} x\right) = 0
11 \log_{5} \left(x - 12\right) = 33
4 \log_{3} \left( 2 x + 1\right) - 2 = 6
Solve for x in each of the following logarithmic equations:
3 \log x = \log 125
\log_{5} \left( 4 x^{2}\right) - \log_{5} x = 3
\log_{10} x + \log_{10} 6 = \log_{10} 48
\log_{10} x - \log_{10} 38 = \log_{10} 37
\log \left(x + 7\right) = \log x + \log 3
\log_{10} 12 + \log_{10} x = \log_{10} \left(x + 6\right)
\log \left(x + 9\right) - \log 2 = \log \left( 7 x + 3\right)
\log \left( 14 x - 2\right) - \log \left( 5 x - 2\right) = \log 3
\log_{8} \left( 5 x + 12\right) = \log_{8} \left(x + 6\right) - \log_{8} 3
\log_{2} \left(\sqrt{ 2 x^{3}}\right) + 1 = 4.5
\log_{7} \left(2 x\right) + \log_{7} 3 = 3
\log_{3} \left(8 x\right) - \log_{3} 40 = 2
\log_{4} 45 - \log_{4} \left( 9 x\right) = 2
\log_{5} \left(x + 12\right) - \log_{5} \left(x - 10\right) = 2
\log_{3} x + \log_{3} \left( 25 x\right) = 8
Solve for x in each of the following logarithmic equations:
\log \left(x + 5\right) + \log \left(x - 2\right) = \log 8
\log_{6} x = \sqrt{\log_{6} x}
\log x + \log \left(x + 3\right) = 1
\log_{10} x + \log_{10} \left(x - 15\right) = 2
\log_{4} x + \log_{4} \left(x - 60\right) = 4
\log_{4} \left(x + 3\right) + \log_{4} \left(x - 3\right) = 2
\log_{7} \left(x + 2\right) + \log_{7} \left(x + 6\right) = \log_{7} 32