Question 172949
Evaluate: Remember, "the logarithm of a number is the power to which the base must be raised to equal the number".
{{{Log[3](81) = x}}} Rewrite in exponential form:
{{{3^x = 81}}} Substitute:{{{81 = 3^4}}}
{{{3^x = 3^4}}} The bases (3) are equal, so the exponents are equal.
{{{highlight(x = 4)}}}
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{{{Log[5](1/25) = x}}} Rewrite in exponential form:
{{{5^x = 1/25}}} Substitute:{{{1/25 = 1/5^2}}}={{{5^(-2)}}} 
{{{5^x = 5^(-2)}}} The bases are equal, so the exponents are equal.
{{{highlight(x = -2)}}}
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{{{ln(e^4) = x}}} Apply the "power rule" for logarithms:
{{{4*ln(e) = x}}} Substitute {{{ln(e) = 1}}}
{{{4 = x}}} or {{{highlight(x = 4)}}}
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{{{Log(0.01) = x}}} Rewrite in exponential form:
{{{10^x = 0.01}}} Substitute {{{0.01 = 1/100}}}={{{1/10^2 = 10^(-2)}}}
{{{10^x = 10^(-2)}}} The bases are equal, so the exponents are equal.
{{{highlight(x = -2)}}}