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olasank [31]
3 years ago
5

If 10^y=y^10, then what is y?

Mathematics
1 answer:
Andrew [12]3 years ago
8 0

Answer:

1

Step-by-step explanation:

10 to the power of 1 is 1, 1 to the power of 10 is still 1

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3 0
3 years ago
X^-2+4x^-1+3=0 solve by making appropriate substitution
Alex

ANSWER

x =  - 1 \: or \: x =  -  \frac{1}{ 3}

EXPLANATION

The given equation is:

{x}^{ - 2}  + 4 {x}^{ - 1}  + 3 = 0

Recall that:

{a}^{ - m}  =  \frac{1}{ {a}^{m} }

\frac{1}{ {x}^{2} }  +  \frac{4}{x}  + 3 = 0

Or

{( \frac{1}{x} )}^{2}  + 4( \frac{1}{x} ) + 3 = 0

Let

u =  \frac{1}{x}

Our equation then becomes:

{u}^{2}  + 4u + 3 = 0

The factors of 3 that add up to 4 are:

{u}^{2}  + 3u + u + 3

u(u + 3) + 1(u + 3) = 0

(u + 1)(u + 3) = 0

u + 1 = 0 \: or \: u + 3 = 0

u =  - 1 \: or \: u =  - 3

This implies that:

\frac{1}{x}  =  - 1 \: or \:  \frac{1}{x}  =  - 3

x =  - 1 \: or \: x =  -  \frac{1}{ 3}

7 0
3 years ago
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