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Contact [7]
3 years ago
10

Write the log equation as an exponential equation

Mathematics
1 answer:
lana [24]3 years ago
8 0

Answer:

\displaystyle  {9}^{2x  - 1}  = 2

Step-by-step explanation:

we are given a logarithmic equation

\displaystyle   \log_{9}(2)  = 2x - 1

we want to rewrite it as exponential equation

remember that,

\displaystyle\log_{a}(b)  = c \iff {a}^{c}  = b

here our a is 9,b is 2 and c is 2x-1

altogether

our exponential equation is

\displaystyle  {9}^{2x  - 1}  = 2

and we're done!

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C gives you 90.2

Step-by-step explanation:

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Evaluate the equation 4K-10/k=8
solong [7]

Answer:

k = 1 + sqrt(7/2) or k = 1 - sqrt(7/2)

Step-by-step explanation:

Solve for k over the real numbers:

4 k - 10/k = 8

Bring 4 k - 10/k together using the common denominator k:

(2 (2 k^2 - 5))/k = 8

Multiply both sides by k:

2 (2 k^2 - 5) = 8 k

Expand out terms of the left hand side:

4 k^2 - 10 = 8 k

Subtract 8 k from both sides:

4 k^2 - 8 k - 10 = 0

Divide both sides by 4:

k^2 - 2 k - 5/2 = 0

Add 5/2 to both sides:

k^2 - 2 k = 5/2

Add 1 to both sides:

k^2 - 2 k + 1 = 7/2

Write the left hand side as a square:

(k - 1)^2 = 7/2

Take the square root of both sides:

k - 1 = sqrt(7/2) or k - 1 = -sqrt(7/2)

Add 1 to both sides:

k = 1 + sqrt(7/2) or k - 1 = -sqrt(7/2)

Add 1 to both sides:

Answer: k = 1 + sqrt(7/2) or k = 1 - sqrt(7/2)

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110

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