[tex]x = p log_{21}(49) = p \frac{ log_{7}(49) }{ log_{7}(21) } = p \frac{2}{ log_{7}(3 \times 7) } = p \frac{2}{ log_{7}(3) + log_{7}(7) } = p \frac{2}{ log_{3}(7) + 1 } = \frac{2p}{ log_{3}(7) + 1 } [/tex]
[tex]x = \frac{2p}{ log_{3}(7) + 1} \\ x log_{3}(7) + x = 2p \\ x log_{3}(7) = 2p - x \\ log_{3}(7) = \frac{2p - x}{x} = \frac{ - x + 13}{ x + 0} [/tex]
[tex]a = - 1 \\ b = 13 \\ c = 1 \\ d = 0[/tex]
a + c = 0
b + d = 13
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Verified answer
[tex]x = p log_{21}(49) = p \frac{ log_{7}(49) }{ log_{7}(21) } = p \frac{2}{ log_{7}(3 \times 7) } = p \frac{2}{ log_{7}(3) + log_{7}(7) } = p \frac{2}{ log_{3}(7) + 1 } = \frac{2p}{ log_{3}(7) + 1 } [/tex]
[tex]x = \frac{2p}{ log_{3}(7) + 1} \\ x log_{3}(7) + x = 2p \\ x log_{3}(7) = 2p - x \\ log_{3}(7) = \frac{2p - x}{x} = \frac{ - x + 13}{ x + 0} [/tex]
[tex]a = - 1 \\ b = 13 \\ c = 1 \\ d = 0[/tex]
a + c = 0
b + d = 13