Is this true? log(x) = logb(c) * log(x). For this question, first try several examples. Then prove it. See the proofs in the Basic Math lecture for ideas. (Hint: let
m = logb(x) and n=logb(c) and p = logc(x). Then use the definition of logarithms and rules of exponents to show m = np.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the base b of another fixed number, the logarithm of a given number x, is the exponent that must be raised in order to obtain the given number x.

The exponential equation logₓy=n is equivalent to xⁿ=y.

The properties of Logarithmic equations are:

log x + log y = log xy
log x-log y= log (x/y)
log ₙn=1
n log x = log xⁿ
[tex]log_ab=\frac{log_xa}{log_xb}[/tex] , x≠0

Now the given expression is of the form: [tex]log_bx=log_bc \cdot log_cx[/tex]

We know that [tex]log_bc=\frac{log_nc}{log_nb}[/tex] and [tex]log_cx=\frac{log_cx}{log_nc}[/tex]

let n=[tex]log_bc=\frac{log_nc}{log_nb}[/tex] and p=[tex]log_cx=\frac{log_cx}{log_nc}[/tex]

Now for the right side of the equation we have:

n×p

[tex]log_bc \cdot log_cx[/tex]

This can be written as:

[tex]or, \frac{log_nc}{log_nb}\cdot\frac{log_cx}{log_nc}\\or, \frac{log_cx}{log_nb}\\or, log_bx[/tex]

which is equivalent to the left side of the equation.

Hence the statement [tex]log_bx=log_bc \cdot log_cx[/tex] is true.

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Is this true? log(x) = logb(c) * log(x). For this question, first try several examples. Then prove it. See the proofs in the Basic Math lecture for ideas. (Hint: let m = logb(x) and n=logb(c) and p = logc(x). Then use the definition of logarithms and rules of exponents to show m = np.

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Is this true? log(x) = logb(c) * log(x). For this question, first try several examples. Then prove it. See the proofs in the Basic Math lecture for ideas. (Hint: let
m = logb(x) and n=logb(c) and p = logc(x). Then use the definition of logarithms and rules of exponents to show m = np.