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Example-13

Solve 3^x = 5^{x − 2}

Solution :

xlog₁₀3 = (x −2) log₁₀5

xlog₁₀3 = xlog₁₀5 − 2log₁₀5

xlog₁₀5 − 2log₁₀5 = xlog₁₀3

xlog₁₀5 − xlog₁₀3 = 2log₁₀5

x(log₁₀5 − log₁₀3) = 2log₁₀5

∴ x = 2log ₁₀5 ÷ (log₁₀5 − log₁₀3)

Example-14

Find x if 2log5 + (1÷ 2) log 9 − log3 = logx

Solution:

logx = 2log5 + (1÷ 2) log 9 − log3

= log5² + log9^{(1 ÷ 2)} − log3

= log 25 + log √9 − log3

= log25 + log 3 − log3

logx = log 25

∴ x = 25

Exercise-1.5

1.Determine the value of the folloing.

i.log ₂₅ 5 ii.log ₈₁3 iii.log ₂ 1 ÷16 iv.log ₇1 v.log _x&radic vi.log ₁₀ 0.01 vii.log _{2 ÷3} 8 ÷27 viii.2 ^{2 + log₂3}

2. Write the following expressions as log N and find their values.

log 2 + log 5

log ₂16 − log ₂2

3 log ₆₄ 4

2 log 3 − 3 log 2

log 10 + 2 log 3 − log 2

page no:25
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