Question

find log 3*log 2*log 625 to the base of √5​

Answer 1

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Precalculus

Evaluate log base 5 of 625

log5(625)log5(625)

Rewrite as an equation.

log5(625)=xlog5(625)=x

Rewrite log5(625)=xlog5(625)=x in exponential form using the definition of a logarithm. If xx and bb are positive real numbers and bb does not equal 11, then logb(x)=ylogb(x)=y is equivalent to by=xby=x.

5x=6255x=625

Create equivalent expressions in the equation that all have equal bases.

5x=545x=54

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

x=4x=4

The variable xx is equal to 44.

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