Jika 4loga = p dan 8 log b = q
maka tentukanlah
![\sqrt{a^5 \sqrt[3]{b\sqrt{a^5 \sqrt[3]{b\sqrt{a^5 \sqrt[3]{b\sqrt{a^5 \sqrt[3]{b}}}}}}}} ~.....](https://tex.z-dn.net/?f=+%5Csqrt%7Ba%5E5+%5Csqrt%5B3%5D%7Bb%5Csqrt%7Ba%5E5+%5Csqrt%5B3%5D%7Bb%5Csqrt%7Ba%5E5+%5Csqrt%5B3%5D%7Bb%5Csqrt%7Ba%5E5+%5Csqrt%5B3%5D%7Bb%7D%7D%7D%7D%7D%7D%7D%7D+%7E..... "\sqrt{a^5 \sqrt[3]{b\sqrt{a^5 \sqrt[3]{b\sqrt{a^5 \sqrt[3]{b\sqrt{a^5 \sqrt[3]{b}}}}}}}} ~.....")
dalam p dan q
maka tentukanlah
dalam p dan q
Mujee
![\displaystyle ^4\log a = p\rightarrow a=4^p=2^{2p}\\^8\log b=q\rightarrow b=8^q=2^{3q}\\\text{soal dapat kita ubah menjadi:}\\\\\\\sqrt{2^{10p} \sqrt[3]{2^{3q}\sqrt{2^{10p}\sqrt[3]{2^{3q}}...}}}=x~~~~(kuadratkan)\\\\2^{10p}.2^{q}x=x^2\\\\x^2-2^{10p+q}x=0\\\\x(x-2^{10p+q})=0\\\\x=0\ (tidak\ memenuhi)\\\\\boxed{x=2^{10p+q}}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5E4%5Clog+a+%3D+p%5Crightarrow+a%3D4%5Ep%3D2%5E%7B2p%7D%5C%5C%5E8%5Clog+b%3Dq%5Crightarrow+b%3D8%5Eq%3D2%5E%7B3q%7D%5C%5C%5Ctext%7Bsoal+dapat+kita+ubah+menjadi%3A%7D%5C%5C%5C%5C%5C%5C%5Csqrt%7B2%5E%7B10p%7D+%5Csqrt%5B3%5D%7B2%5E%7B3q%7D%5Csqrt%7B2%5E%7B10p%7D%5Csqrt%5B3%5D%7B2%5E%7B3q%7D%7D...%7D%7D%7D%3Dx%7E%7E%7E%7E%28kuadratkan%29%5C%5C%5C%5C2%5E%7B10p%7D.2%5E%7Bq%7Dx%3Dx%5E2%5C%5C%5C%5Cx%5E2-2%5E%7B10p%2Bq%7Dx%3D0%5C%5C%5C%5Cx%28x-2%5E%7B10p%2Bq%7D%29%3D0%5C%5C%5C%5Cx%3D0%5C+%28tidak%5C+memenuhi%29%5C%5C%5C%5C%5Cboxed%7Bx%3D2%5E%7B10p%2Bq%7D%7D "\displaystyle ^4\log a = p\rightarrow a=4^p=2^{2p}\\^8\log b=q\rightarrow b=8^q=2^{3q}\\\text{soal dapat kita ubah menjadi:}\\\\\\\sqrt{2^{10p} \sqrt[3]{2^{3q}\sqrt{2^{10p}\sqrt[3]{2^{3q}}...}}}=x~~~~(kuadratkan)\\\\2^{10p}.2^{q}x=x^2\\\\x^2-2^{10p+q}x=0\\\\x(x-2^{10p+q})=0\\\\x=0\ (tidak\ memenuhi)\\\\\boxed{x=2^{10p+q}}")
3 votes
Thanks 9