Hvordan løser vi denne?
lg x^3 + 2lg3x = 4
Logaritmisk ligning
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Nå er
lg x[sup]3[/sup] + 2 lg 3x = lg x[sup]3[/sup] + lg (3x)[sup]2[/sup] = lg x[sup]3[/sup] + lg 9x[sup]2[/sup] = lg (x[sup]3[/sup]*9x[sup]2[/sup]) = lg 9x[sup]5[/sup], dvs. at
lg 9x[sup]5[/sup] = 4
9x[sup]5[/sup] = 10[sup]4[/sup]
x[sup]5[/sup] = 10[sup]4[/sup]/9
x = (10[sup]4[/sup]/9)[sup]1/5[/sup] ≈ 4,07.
lg x[sup]3[/sup] + 2 lg 3x = lg x[sup]3[/sup] + lg (3x)[sup]2[/sup] = lg x[sup]3[/sup] + lg 9x[sup]2[/sup] = lg (x[sup]3[/sup]*9x[sup]2[/sup]) = lg 9x[sup]5[/sup], dvs. at
lg 9x[sup]5[/sup] = 4
9x[sup]5[/sup] = 10[sup]4[/sup]
x[sup]5[/sup] = 10[sup]4[/sup]/9
x = (10[sup]4[/sup]/9)[sup]1/5[/sup] ≈ 4,07.