Question

Solve. 64^x= 16^(x–1)

Answer 1

\[\large 64^x = 16^{x-1} \implies 4^{3x} = 4^{2(x-1)} \implies 4^{3x} = 4^{2x-2}\]

Just equate the exponents or powers and find x..

Answer 2

can you rewrite the 64 and 16 as powers with base 2?

Answer 3

or do as in waterin eyes case, base 4....

Answer 4

What do you mean equate the exponents or powers?

Answer 5

What are the exponents tell me on LHS as well as on RHS first tell me this..

Answer 6

Rule: -\[\huge{a^x=a^y \implies x=y.}\]

Answer 7

\[\huge (x)^a = (x)^b \implies \color{blue}{a = b}\]

Answer 8

So just equate the coefficients there..

Equate means just make them equal or between them use "=" and then solve for x.

Answer 9

*exponents not coefficient..

Answer 10

So 3x=2x-2?

Answer 11

Go ahead..

Answer 12

Yes you are right... @HayleyWhite17

Answer 13

6x-6?

Answer 14

How ??

Answer 15

\(3x = 2x - 2\)

Subtract 2x both the sides and tell me what do you get ??

Answer 16

Ok hold on