Tough Logarithm Expression Questions in Arithmetic Form with Solutions

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Prove $\log{(1+2+3)}$ $\,=\,$ $\log{(1)}$ $+$ $\log{(2)}$ $+$ $\log{(3)}$

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Evaluate $5\cos{x}$ $-$ $12\sin{x}$, if $5\sin{x}$ $+$ $12\cos{x}$ $=$ $13$

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