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To solve this type of question, we want to take logarithms of both sides of the equation in order to try to isolate x.

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For example, if we have $a^x = b$ then we proceed as above to get $x\\log{a} = \\log{b}$ and hence $x = \\frac{\\log{a}}{\\log{b}}$

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Laws of logarithms are useful here:

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$\\log{a} + \\log{b} = \\log{ab}$

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$\\log{a} - \\log{b} = \\log{\\frac{a}{b}}$

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$\\log{a^n} = n\\log{a}$

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$\\var{a1}^x = \\var{a2}$

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$x=$$\\log_{10}$[[0]]$\\log_{10}$[[1]]

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or

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$x=\\log_{\\var{a1}}$[[2]]

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$\\var{b1}^x=\\var{b2}$

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$x=$[[0]]

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$\\var{c1}^x = \\var{c2}$

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$x=$[[0]]

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$\\var{d1}^{x-1} = \\var{d2}^{x+1}$

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([[1]])$\\simplify{log({d1})}=$([[2]])$\\simplify{log({d2})}$

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Hence $x=$[[0]]

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$\\var{e1}^{\\simplify{{e3}x-{e4}}} = \\var{e2}^{\\simplify{{e5}x+{e6}}}$

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$x=$[[0]]

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$\\var{f1}^{\\simplify{{f3}x-{f4}}} = \\var{f2}^{\\simplify{{f5}x}}$

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$x=$[[0]]

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Solve each of the following equations for $x$, giving your answers in terms of base 10 logarithms OR to 3 decimal places.

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Remember to write $\\simplify{log(a)}$ you must type loga with brackets around the a.

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