# How do you solve # 8^(6x-5)=(1/16)^(6x-2)#?

##### 2 Answers

Mar 3, 2016

x =

#### Explanation:

Express 8 and 16 in powers of 2. cross multiply.

Mar 3, 2016

#### Explanation:

We will write

#8=2^3#

#1/16=1/2^4=2^-4#

The equation can then be rewritten as

#(2^3)^(6x-5)=(2^-4)^(6x-2)#

We then use the rule:

#(a^b)^c=a^(bc)#

This makes the equation

#2^(3(6x-5))=2^(-4(6x-2))#

Since the bases are equal, the exponents can be set equal to one another as well:

#3(6x-5)=-4(6x-2)#

#18x-15=-24x+8#

#42x=23#

#x=23/42#