# Tricky Logarithm Problem…

Find the exact solution to the equation ${ 3 }^{ x }{ e }^{ 7x+2 }=15$. ${ 3 }^{ x }{ e }^{ 7x+2 }=15\\ \\ { 3 }^{ x }{ e }^{ 7x }{ e }^{ 2 }=15\\ \\ { 3 }^{ x }{ e }^{ 7x }=\frac { 15 }{ { e }^{ 2 } } \\ \\ { \left( 3{ e }^{ 7 } \right) }^{ x }=\frac { 15 }{ { e }^{ 2 } } \\ \\ \log _{ e }{ \left( { \left( 3{ e }^{ 7 } \right) }^{ x } \right) } =\log _{ e }{ \left( \frac { 15 }{ { e }^{ 2 } } \right) } \\ \\ x\log _{ e }{ \left( 3{ e }^{ 7 } \right) } =\log _{ e }{ \left( \frac { 15 }{ { e }^{ 2 } } \right) } \\ \\ x=\frac { \log _{ e }{ \left( \frac { 15 }{ { e }^{ 2 } } \right) } }{ \log _{ e }{ \left( 3{ e }^{ 7 } \right) } } =\frac { \log _{ e }{ 15-\log _{ e }{ \left( { e }^{ 2 } \right) } } }{ \log _{ e }{ 3+\log _{ e }{ \left( { e }^{ 7 } \right) } } } =\frac { \ln { 15-2\log _{ e }{ \left( e \right) } } }{ \ln { 3+7\log _{ e }{ \left( e \right) } } } \\ \\ =\frac { \ln { 15-2 } }{ \ln { 3+7 } } ,\quad \therefore \quad x=\frac { -2+\ln { 15 } }{ 7+\ln { 3 } } \\$

# (a+b)(a-b)=a^2-b^2 (The Real Proof) (Difference Of Two Squares Demystified)

Ever wondered why (a+b)(a-b)=a^2-b^2? The videos below will reveal to you why we accept this fact. Enjoy!

1) Why (a+b)(a+b)=a^2+2ab+b^2

2) Why (a+b)(a-b)=a^2-b^2

# How To Come Up With The Quadratic Formula – From Scratch

Learn how to come up with the quadratic formula from scratch. Watch the video below…

# FREE MATHS VIDEOS – FOR A LEVEL & GCSE STUDENTS

Welcome to MathsVideos.net. On this website you will find maths videos containing tricks and advice that you can use to pass your maths exams. MathsVideos.net was recently created in January 2014. These videos are produced by a student who is doing his A-Levels in the UK.

# Find The Formula For The Volume Of Cones

Find the volumes of cones formula using differentiation and integration. This playlist will show you how to come up with the volumes of cones formula from scratch. Knowledge about how to differentiate and integrate required.