Question

14. Without using log tables, find x if
half of log10(11+4√17)= log10 (2+x)
Hint.

Answer 1

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Answer 2

ATQ

(1/2)log10(11+4√17)=

log10(2+x)

log10(11+4√17)=

2 log10(2+x)

log10(11+4√17)=

log10(2+x)^2

(11+4√17)=(2+x)^2

11+4√17=x^2+4x+4

0=x^2+4x-(7+4√17)

Using quadratic equation,

x={-4(+,-)√(16+28+16√17)}/2

x={-4(+,-)√(44+16√17)}/2

x={-4(+,-)2√(11+4√17)}/2

x={-2(+,-)√(11+4√17)}

x= -2+√[11+4√17] or

-2-√[11+4√17]

Exact values,

x=3.2433 or -7.2433