All categories

3 years ago

Solving Exponential Equations (lacking a common base) 4^x-5=8

Mathematics

2 answers:

avanturin [10]3 years ago

8 0

Answer:

x= 6 1/2 or 6.5

Step-by-step explanation:

4^x-5 =8

2^2(x-5) =2^3

since the base is equal, the powers are equal

2(x-5) = 3

2x - 10 = 3

2x = 3 + 10

2x = 13

2x/2 = 13/2

x = 6 1/2 or 6.5

Tju [1.3M]3 years ago

6 0

Answer:

6.5

Step-by-step explanation:

4^(x-5) = 8

2^[2(x-5)] = 2³

Equating powers:

2(x-5) = 3

x-5 = 3/2

x = 13/2 or 6½

You might be interested in

What is the probability of pulling out a red marble then a blue marble?

statuscvo [17]

Answer:

Step-by-step explanation:

Total marble = 8+5+4 = 19

n(Y) = 8, n(B) = 4 and n(R) = 5

Prob(R) = 5/17

Prob(B) = 4/16 {one marble is pulled out already}

Prob(R and B) = 5/17 × 4/16

= 5/17 × 1/4

= 5/68

5 0

2 years ago

When david emptied the collection canister of his vacuum cleaner, he found nickels and quarters among the other of the canister.

Ugo [173]

he has 9 quarters and 12 nickles.

5 0

3 years ago

How do I expand the following equation with the binomial theorem?

Vsevolod [243]

Answer:

16x^4+32x^3+24x^2+8x+1

Step-by-step explanation:

(2x+1)^4

(2x+1)*(2x+1)*(2x+1)*(2x+1)

4 0

2 years ago

On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is

OlgaM077 [116]

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.

$P(x,y)$ - Original point.

$k$ - Scale factor.

$P'(x,y)$ - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

( $P(x,y) = (10, 40)$ , $Q(x,y) = (70, 120)$ , $O(x,y) = (0,0)$ , $k = 5$ )

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$

$P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]$

$P'(x,y) = (50,200)$

$Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]$

$Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]$

$Q'(x,y) = (350, 600)$

Then, the length of the resulting segment is determined by following Pythagorean identity:

$l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}$

$l_{P'Q'} = 500$

The length of the resulting segment is 500.

3 0

2 years ago

If f(x) =5x-1 , then f(3)=

stich3 [128]

$\text{If f(x) =5x-1 , then f(3)=
} \\\\ f(3)=5 \cdot 3 -1 \\ f(3)=15-1 \\ f(3)=14$

8 0

3 years ago