Posted by **Mc78** on Sunday, January 1, 2012 at 6:12pm.

Use the properties of logarithms to find the exact value of the expression log[16]4*log[5]57

- Logarithms -
**drwls**, Sunday, January 1, 2012 at 8:05pm
What is 57 ?

- Logarithms -
**Hunter**, Sunday, January 1, 2012 at 8:40pm
suppose to be SQRT7

- Logarithms -
**Reiny**, Sunday, January 1, 2012 at 8:46pm
is that 5√7 or √7 ?

log_{16}4 = 1/2

log_{5} 5√7 is not exact

was that base supposed to be 7 ?

- Logarithms -
**Mc78**, Sunday, January 1, 2012 at 9:00pm
log[16]4*log[5]57 is what the question, I am unsure how to solve exact

- Logarithms -
**Mc78**, Sunday, January 1, 2012 at 9:01pm
log[16]4*log[5]5sqrt7

- Logarithms -
**Reiny**, Sunday, January 1, 2012 at 9:05pm
log[16]4*log[5]5sqrt7

= (1/2(*(log[5]5 + log[5]√7)

= (1/2)( 1 + (1/2)log[5] 7)

= 1/2 + (1/4) log_{5}7

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