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Question Number 182737 by cortano1 last updated on 13/Dec/22

Answered by dre23 last updated on 14/Dec/22

$$d=\frac{ln\left(y\right)}{ln\left(z\right)}-\frac{ln\left(x\right)}{ln\left(y\right)}=-15\frac{ln\left(z\right)}{ln\left(x\right)}-\frac{ln\left(y\right)}{ln\left(z\right)}=\frac{ln\left(x\right)}{ln\left(y\right)}-1=d$$$$d+1=\frac{ln\left(x\right)}{ln\left(y\right)}$$$$\frac{ln\left(y\right)}{ln\left(z\right)}=2d+1$$$$-15\frac{ln\left(z\right)}{ln\left(x\right).}=3d+1$$$$\frac{ln\left(x\right)}{ln\left(z\right)}=-\frac{15}{(1+3d)}=(d+1)(2d+1)$$$$\iff 6d^3+11d^2+6d+16=0$$$$$$$$$$

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