Laws of Indices

[Mish1]

I know the answers to Q6 c,d&e are -5/2, -1/4, & -1/2....I just don't know how they got them??? Any help gratefully received!

 

[MarkFL]

c) [MATH]\sqrt{5}\times5^x=\frac{1}{25}[/MATH]
Rewrite both sides as powers of 5:

[MATH]5^{x+\frac{1}{2}}=5^{-2}[/MATH]
Equate exponents:

[MATH]x+\frac{1}{2}=-2[/MATH]
[MATH]x=-\frac{5}{2}[/MATH]
Can you use a similar method for the other two equations?

 

[Mish1]

c) [MATH]\sqrt{5}\times5^x=\frac{1}{25}[/MATH]
Rewrite both sides as powers of 5:

[MATH]5^{x+\frac{1}{2}}=5^{-2}[/MATH]
Equate exponents:

[MATH]x+\frac{1}{2}=-2[/MATH]
[MATH]x=-\frac{5}{2}[/MATH]
Can you use a similar method for the other two equations?

Thank you Mark