QR problems about exponentials

[ysk]

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Can anyone explain these questions?

1. Solve for 27^(2x) = 3^(3x-5)

A. -3/5
B. -5/3
C. 5
D. -5
E. 15


2. If x^(-2/3) = 4, then x =

A. 1/8
B. 8
C. -1/8
D. 4
E. -4


The answers are B and A. I can figure it out by looking at the choices but I can't just solve it. Can anyone help me out?

 

[grmaster1]

Can anyone explain these questions?

1. Solve for 27^(2x) = 3^(3x-5)

A. -3/5
B. -5/3
C. 5
D. -5
E. 15


2. If x^(-2/3) = 4, then x =

A. 1/8
B. 8
C. -1/8
D. 4
E. -4


The answers are B and A. I can figure it out by looking at the choices but I can't just solve it. Can anyone help me out?

1. (3^3)^2x=3^(3x-5) make common bases

6x=3x-5

x=-5/3

2. (x^-2/3)^-3/2=4^-3/2 get rid of exponent for unknown

x=1/(4^1/2)^3=1/8 rules of exponents

Why would you clutter your head with this garbage anyway?

 

[joonkimdds]

Why would you clutter your head with this garbage anyway?

is there any possibility that DAT will have these simple problems?

 

[duh?]

27^(2x)= 3^(3x-5)
3^3(2x)=3^(3x-5)
3^6x=3^(3x-5)
6x=3x-5
6x-3x=-5
3x=-5
x=-5/3

It is quite scary that cannot figure out #2 and my DAT is in 2 weeks! 😱

 

[joonkimdds]

27^(2x)= 3^(3x-5)
3^3(2x)=3^(3x-5)
3^6x=3^(3x-5)
6x=3x-5
6x-3x=-5
3x=-5
x=-5/3

It is quite scary that cannot figure out #2 and my DAT is in 2 weeks! 😱

it's like what GRmaster said.

2. (x^-2/3)^-3/2=4^-3/2 get rid of exponent for unknown

x=1/(4^1/2)^3=1/8 rules of exponents

Why would you clutter your head with this garbage anyway?


1st step = ger rid of exponent
since exponent is minus the entire thing is 1 over entire thing
square root of 4 is 2, then 2 cube = 8
since 8 is denominator ...it's 1/8

 

[duh?]

Thanks. my post came in kinda late, when i answered y'all hadn't 'inputted' yet! 😀

 

[ysk]

cool thanks!