log(x)=-2.593e-4 can someone help me find antilog Solution FOLLOW THIS When b is
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log(x)=-2.593e-4 can someone help me find antilogExplanation / Answer
FOLLOW THIS When b is raised to the power of y is equal x: b y = x Then the base b logarithm of x is equal to y: logb(x) = y For example when: 24 = 16 Then log2(16) = 4 Logarithm as inverse function of exponential function The logarithmic function, y = logb(x) is the inverse function of the exponential function, x = by So if we calculate the exponential function of the logarithm of x (x>0), f (f -1(x)) = blogb(x) = x Or if we calculate the logarithm of the exponential function of x, f -1(f (x)) = logb(bx) = x Natural logarithm (ln) Natural logarithm is a logarithm to the base e: ln(x) = loge(x) When e constant is the number: See: Natural logarithm Inverse logarithm calculation The inverse logarithm (or anti logarithm) is calculated by raising the base b to the logarithm y: x = log-1(y) = b y Logarithmic function The logarithmic function has the basic form of: f (x) = logb(x) Logarithm rules Rule name Rule Logarithm product rule logb(x · y) = logb(x) + logb(y) Logarithm quotient rule logb(x / y) = logb(x) - logb(y) Logarithm power rule logb(x y) = y · logb(x) Logarithm base switch rule logb(c) = 1 / logc(b) Logarithm base change rule logb(x) = logc(x) / logc(b) Derivative of logarithm f (x) = logb(x) ? f ' (x) = 1 / ( x ln(b) ) Integral of logarithm ? logb(x) dx = x · ( logb(x) - 1 / ln(b) ) + C Logarithm of negative number logb(x) is undefined when x = 0 Logarithm of 0 logb(0) is undefined Logarithm of 1 logb(1) = 0 Logarithm of the base logb(b) = 1 Logarithm of infinity lim logb(8) = 8, when x?8 See: Logarithm rules Logarithm product rule The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. logb(x · y) = logb(x) + logb(y) For example: log10(3 · 7) = log10(3) + log10(7) Logarithm quotient rule The logarithm of the division of x and y is the difference of logarithm of x and logarithm of y. logb(x / y) = logb(x) - logb(y) For example: log10(3 / 7) = log10(3) - log10(7) Logarithm power rule The logarithm of x raised to the power of y is y times the logarithm of x. logb(x y) = y · logb(x) For example: log10(28) = 8 · log10(2) Logarithm base switch rule The base b logarithm of c is 1 divided by the base c logarithm of b. logb(c) = 1 / logc(b) For example: log2(8) = 1 / log8(2) Logarithm base change rule The base b logarithm of x is base c logarithm of x divided by the base c logarithm of b. logb(x) = logc(x) / logc(b) For example, in order to calculate log2(8) in calculator, we need to change the base to 10: log2(8) = log10(8) / log10(2) See: log base change rule Logarithm of negative number The base b logarithm of x when xRelated Questions
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