Question

Help.

Answer 1

If
\[a ^{x + 1}/b ^{x + 1} = 10\]
solve for x.

Answer 2

I am confused because it has not been mentioned whether to find as a constant or in terms of a and b.

Answer 3

take log
u can find x in terms of a and b

Answer 4

Can you please show me how to start?

Answer 5

\[(\frac{a}{b})^{x+1}=10 \\ \log (\frac{a}{b})^{x+1} = \log 10=1 \\ (x+1) \log \frac{a}{b} =1\]

Answer 6

How is
\[\log(a/b)^{x + 1} = \log10 = 1\]?

Answer 7

exactly
what then?

Answer 8

I'm asking how it can be equal to one?

Answer 9

log 10 =1

Answer 10

because 10^1=10

Answer 11

Oh I get it ...

Answer 12

u must know this property of log
\[\huge \log b^a = a \log b\]

Answer 13

Yes I know .... but I still don't know how to solve an equation involving log.

Answer 14

\[(x + 1)\log (a/b) = 1\]
What next?

Answer 15

well note that u should treat ***log (a/b)*** like a constant now because a,b are constants

Answer 16

So (x + 1) * some constant = 1.

Answer 17

exactly

Answer 18

so how to proceed?

Answer 19

\[x=\frac{1}{\log \frac{a}{b}}-1\]

Answer 20

c=log (a/b)

(x+1)*c=1

x+1=1/c

x=(1/c)-1