# How do you solve #3^(4x) = 3^(5-x)#?

##### 3 Answers

#### Explanation:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note that

Write as

Multiply both sides by

But

Comparing just the indices

Notice from the outset that the two exponents must be equal, since their bases are both

#color(red)3^color(blue)(4x)=color(red)3^color(blue)(5-x)" "=>" "color(blue)(4x)=color(blue)(5-x)" "=>" "5x=5#

Thus,

#### Explanation:

As a Real-valued function of Real numbers,

So

Add

#5x=5#

Divide both sides by

#x=1#