Question

# If where determine b –

- 25
- 5
- 625
- 16

Hint:

### logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if , in which case one writes x = .

## The correct answer is: 5

### If where determine b –

Just like we can change the base b for the exponential function, we can also change the base b for the logarithmic function. The logarithm with base b is defined so that

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Given that and then value of equals –

These four basic properties all follow directly from the fact that logs are exponents.

log_{b}(*xy*) = log_{b}*x* + log_{b}*y*.

log_{b}(*x/y*) = log_{b}*x* - log_{b}*y*.

log_{b}(*x ^{n}*) =

*n*log

_{b}

*x*.

log

_{b}

*x*= log

_{a}

*x*/ log

_{a}

*b*.

Given that and then value of equals –

These four basic properties all follow directly from the fact that logs are exponents.

log_{b}(*xy*) = log_{b}*x* + log_{b}*y*.

log_{b}(*x/y*) = log_{b}*x* - log_{b}*y*.

log_{b}(*x ^{n}*) =

*n*log

_{b}

*x*.

log

_{b}

*x*= log

_{a}

*x*/ log

_{a}

*b*.

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