+26388 7log(3x)+3log(5x)=15 what is x
i assume log is the natural logarithm
\(\begin{array}{|rcll|} \hline 7\cdot log(3x)+3 \cdot log(5x) &=& 15 \\ 7\cdot (~log(3)+log(x) ~)+3 \cdot (~log(5)+log(x) ~) &=& 15 \\ 7\cdot log(3) + 7\cdot log(x) +3\cdot log(5) + 3\cdot log(x)&=& 15 \\ 10\cdot log(x) + 7\cdot log(3) +3\cdot log(5) &=& 15 \\ 10\cdot log(x) + log(3^7) + log(5^3) &=& 15 \\ 10\cdot log(x) + log(3^7\cdot 5^3) &=& 15 \quad & | \quad -log(3^7\cdot 5^3) \\ 10\cdot log(x) &=& 15 -log(3^7\cdot 5^3) \quad & | \quad : 10 \\ log(x) &=& \frac{ 15 -log(3^7\cdot 5^3) } {10 } \\ log(x) &=& \frac{ 15}{10} - \frac{ \log(3^7\cdot 5^3) } {10 } \\ log(x) &=& 1.5 - \frac{ \log(3^7\cdot 5^3) } {10 } \\ log(x) &=& 1.5 - \log(~(3^7\cdot 5^3)^{\frac{1}{10}}~) \\ log(x) &=& 1.5 - \log(3^\frac{7}{10}\cdot 5^\frac{3}{10}) \\ log(x) &=& 1.5 - \log(3^{0.7}\cdot 5^{0.3}) \quad & | \quad e^{()} \\ x &=& e^{1.5 - \log(3^{0.7}\cdot 5^{0.3}) } \\ x &=& e^{1.5} \cdot e^ {- \log(3^{0.7}\cdot 5^{0.3}) } \\ x &=& e^{1.5} \cdot \frac{ 1 } { e^{\log(3^{0.7}\cdot 5^{0.3}) } } \\ x &=& e^{1.5} \cdot \frac{ 1 } { 3^{0.7}\cdot 5^{0.3} } \\ x &=& \frac{ e^{1.5} } { 3^{0.7}\cdot 5^{0.3} } \\ x &=& \frac{ 4.48168907034 } {2.15766927997\cdot 1.62065659669 } \\ x &=& \frac{ 4.48168907034 } {3.49684095207 } \\ \mathbf{x} & \mathbf{=} & \mathbf{1.28163938016178...} \\ \hline \end{array}\)
+14985 7log(3x)+3log(5x)=15 what is x
i assume lg is the 10 - logarithm
\(7(lg3+lgx)+3(lg5+lgx)=15\)
\(7lg3+7lgx+3lg5+3lgx=15\)
\(7lgx+3lgx=15-(7lg3+3lg5)\)
\(lgx^7+lgx^3=15-lg \ 273375\)
\(lg(x^7\times x^3)=15-lg \ 273375\)
\(lgx^{10}=15-lg \ 273375\)
\(lgx^{10}+lg273375=15\)
\(lg \ (273375 \ x^{10})=15\)
\(273375 x^{10}=10^{15}\)
\(\large x^{10}=\frac{10^{15}}{273375}\)
\(\Large x=\sqrt[10]{\frac{10^{15}}{273375}} \)
\(\large x=9.04324132413\)
!
+9665 To asinus:
The 6th step:
\(\lg x^{10} = 15 - \lg 273375\\ 10 \lg x = 15 - \lg 273375\\ x = 10^{\frac{15-\lg 277375}{10}}\)
Because the right hand side is already a numerical value and the left hand side is x, so this can be the solution.
No need to do all that..... LOL
~The smartest cookie in the world
+14985 7log(3x)+3log(5x)=15 what is x
\(7(lg3+lgx)+3(lg5+lgx)=15\)
\(\large x=9.04324132413\)
\(\large 10.03412+4.96588=15\)
!
