# 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…

# How To Come Up With Pythagoras’ Equation

Learn how to come up with Pythagoras’ famous formula – from absolute scratch…

To see the full explanation in writing, please visit the link below:

2 ways to derive Pythagoras’ equation from scratch

# Trapezium Rule Formula – Derivation

Find out how to come up with the Trapezium Rule formula from scratch.

1) Derive the formula for the area of trapeziums:

2) Use the area of trapeziums formula to come up with the Trapezium Rule formula:

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# 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.

# Areas Of Triangles & The Sine Rule

Learn how to come up with the formula for areas of triangles, then use this formula to derive the sine rule formula.

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# 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.