Question

Solve:
(1/10)^y=100^(y+3)

Answer 1

\[(\frac{1}{10})^y = 100^{(y+3)}\]

Some useful properties of exponents:
\[(\frac{a}{b})^n = \frac{a^n}{b^n}\]
\[a^{-n} = \frac{1}{a^n}\]

Answer 2

and \[(ab)^n = a^nb^n\]

Answer 3

just what I was about to add :)

Answer 4

So, I would turn the expression on the left into something more like the expression on the right via the 2nd property

Answer 5

\[1^{y}/10y \] = ....
how do you solve\[100 ^{y+3}\]
with maybe laws of exponents? I'm not sure

Answer 6

****[10^{y}\]

Answer 7

please help:)

Answer 8

Can't you write \[100^{y+3} = 10^{y+3}10^{y+3}\]?

Answer 9

like \[(10^{2})^{y+3}\]?

Answer 10

\[10^{-y}=100^{y+3}=10^{10y+30}\]
thus
\[-y= 10y+30\]

Answer 11

heheh i mean -y=2y+6

Answer 12

Okay, here's how I would do it:
\[y^{-1} = 100^{y+3}\]split rhs
\[y^{-1}=10^{y+3}10^{y+3}\]Multiply both sides by \(10^y\)
\[1= 10^0 =10^y10^{y+3}10^{y+3}\]Log base 10 of both sides
\[0= y+y+3+y+3\]\[y=-2\]

Answer 13

sorry, miswrote the left hand side in the first two lines, should have been \(10^{-y}\)