Logarithm multiplication property error, can't figure out why.

Question

I know there is a mistake and where it is but I can't figure out why.

Equation: $$ 3+2(12^{x+1}) = 291 $$

From here I do: $$ 2(12^{x+1}) = 291-3\\ 2(12^{x+1}) = 288\\ $$

Then I take the natural logarithms on both sides; $$ \ln(2*12^{x+1}) = \ln(288)\\ \ln(2*12^{x+1}) = \ln(2*12^2)\\ $$

Now I apply multiplication property so $\ln(a*b)$ should equal $\ln(a)+\ln(b)$ But here it seems that I'm making a mistake, can't figure out why:

$$ \ln(2) + \ln(12^{x+1}) = \ln(2) + \ln(12^2)\\ $$

subtract $\ln(2)$ on both sides: $$ \ln(12^{x+1}) = \ln(12^2) \\ $$

Then it should be: $$ (x+1) \ln(12) = 2 \ln(12)\\ x+1 = 2\\ x=1\\ $$

but it's not the right result..

Thanks in advance :)

It is the right result: you can check it at once substituting in the original question. Why do you way it isn't? — Timbuc, Sep 14 '14 at 15:34
check your question again since the answer you got is 100% right according to your posted question — Jasser, Sep 14 '14 at 15:37
sorry I was confused by a step by step solver website, I should have checked the equation by myself — complexguest, Sep 14 '14 at 15:46

score 2 · Accepted Answer · answered Sep 14 '14 at 15:36

The equation \begin{align} 3 + 2 \cdot 12^{x+1} = 291 \end{align} leads to \begin{align} 2 \cdot 12^{x+1} &= 291-3 = 288 \\ 12^{x+1} &= 144 = 12^{2} \end{align} for which $x+1 = 2$ by equating the exponents, or taking the logarithm of both sides. The value of $x$ is $x=1$.

Logarithm multiplication property error, can't figure out why.

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