Question

A student is solving the equation 4^x–1 = 64^x+3.
Step 1: 4^x – 1 = 64^x + ^3
Step 2: 4^x – 1 = (43)^x + ^3
Step 3: 4^x – 1 = 43^x + ^9
Which is the next step?
4 = 3x + 9
x - 1 = -(3x + 9)
x - 1 = x + 3
x - 1 = 3x + 9

Answer 1

\[4^{x-1} = 64^{x+3}\]

Answer 2

Step 3: \(\LARGE 4^{x – 1} = 4^{3x + 9} \)

Answer 3

since the bases are equal, exponents also will be equal. So the next step would be to equate the exponents

Answer 4

\[Step 1: 4^{x-1} = 64^{x+3} \]
\[Step 2: 4^{x-1}= (43)^{x+3} \]
\[Step 3: 4^{x-1} = 43^{x+9}\]

Answer 5

It has to be like this :

\[\large Step 1: 4^{x-1} = 64^{x+3}\]
\[\large Step 2: 4^{x-1} = (4^3)^{x+3}\]
\[\large Step 3: 4^{x-1} = 4^{3x+9}\]
\[\large \color{green}{ Step 4:x-1 =3x+9}\]

Answer 6

64 CANNOT become 43 just like that, okay ?

Answer 7

3 needs to be in the exponent : \(\large 64 = 4\times 4\times 4 = 4^3\)

Answer 8

where did the 43 come from?

Answer 9

oh it should be 4^3x

Answer 10

(4^3)^3 to get 4^9 to raise a power to a power multiply

Answer 11

step 4 as given by rsdhvika above choice x-1 = 3x + 9

Answer 12

Thank you!