Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Write yloga(x) - zIn(x^2) -12logb(X)? as a single log base e?

need Help???

do you know the three log laws and the law to change base?

log(a) of x + log(a) of y = log(a) of xy
log(a) of x - log(a) of y = log(a) of x/y
n [log(a) of x] = log(a) of (x^n)

And change of base,

log(a) of x = [log(b) of x]/[log(b) of a]

Using these, you can solve that.

OP

I know the rules, laws wotever but idon't know how to apply it in the context of the question

\log_{a}(x) = \frac{\ln x}{\ln a}

\log_{b}(X) = \frac{\ln X}{\ln b}

y\log_{a}(x) - z\ln(x^2) -12\log_{b}(X) = \\ y \frac{\ln x}{\ln a} - z \ln(x^{2}) - 12 \frac{\ln X}{\ln b} = \\\ln(x^{\frac{y}{\ln a}})-\ln([x^{2}]^{z}) - \ln (X^{\frac{12}{\ln b}})

Now use

\ln a - \ln b = \ln (\frac{a}{b})

to tidy it up. I'd do it, but I've got to go.

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