Question

log*bA=3 log*bC=2 log*bD=5
log*b A^3D^4/C^2

Answer 1

Oh yeah what i meant to add was that we are trying to figure out the value of the second eqution given the values of the a c and d

Answer 2

also the options for answers are
176
25
33
and 4218.75

Answer 3

well apply the log laws for multiplication and addition

log law for division is subtract

\[\log_{b} (\frac{A^3 D^4}{C^2}) = \log_{b} (A^3D^4) - \log_{b} (C^2)\]

then you need the log law for multiplication, which is add the logs

\[\log(AB) = \log(A) + \log(B)\]

so apply this law to the A^3D^4

lastly you need to apply the log law for powers... which needs you to multiply the log by the power

\[\log(x^a) = a \times \log(x)\]

if you can do all that, the last thing will be to substitute the values that have been given and calculate an answer.

Answer 4

So confused! pls explain more:)

Answer 5

@campbell_st

Answer 6

ok... so the next step is

\[\log_{b}(A^3) + \log_{b}(D^4) - \log_{b}(C^2)\]

does that make sense...?

Answer 7

Yes I did that:)

Answer 8

@campbell_st now what

Answer 9

@kenzie.christiansen do you know how to do this

Answer 10

no sorry if i did i could help u but i dont

Answer 11

ok...apply the log law for powers

\[3 \times \log_{b}(A) + 4 \times \log_{b}(D) - 2 \times \log_{b}(C)\]

now substitute your values.