Simple exponentials

Algebra Level 1

Find the value of $x$ satisfying:

$\Large { 3 }^{ { 2 }^{ x } }=6561$

0 3

\frac{1}{2}

2 solutions

Ponhvoan Srey
Oct 6, 2015

${ 3 }^{ { 2 }^{ x } }=6561\\ { 3 }^{ { 2 }^{ x } }={ 3 }^{ 8 }\\ \Longleftrightarrow { 2 }^{ x }=8\\ \boxed { x=3 }$

I looked up about exponents and it said you do them left to right. So you do 3^2 first, which is 9. So you have 9^x=6561, so x=4. Why are the rules not consistent?

Chelsea Saunders - 5 years, 7 months ago

Power towers are always evaluated from the top down. Read more about them here .

Zach Abueg - 3 years, 10 months ago

Jonathan Wallace
Oct 29, 2015

The issue here is that staircasing indices the way it it written here would imply we do $(3^2)^x$ .

Hence we would get: $3^{2x} = 3^8$

So x = 4,

If you are not using the standard notation you should be clearer by writing it as:

$3^{(2^x)}$

This also explain why if you work left to right you get x = 4.

Hope this helps.

Simple exponentials

2 solutions

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