ICSE Class 9 Answered

Find all the values of 'a' for which the following equalities hold true

Asked by kdimple765 | 18 Dec, 2022, 07:10: PM

Expert Answer

To solve the logarithms:

(ii) log_1/3 a = 4

(iii) log_a 1 = 0

(iv) log₃ (a² + 1) = 1

Solution:

left parenthesis ii right parenthesis log subscript 1 divided by 3 end subscript space straight a equals 4 rightwards double arrow open parentheses 1 third close parentheses to the power of log subscript 1 divided by 3 end subscript space straight a end exponent space equals open parentheses 1 third close parentheses to the power of 4 Since comma space straight x to the power of log subscript straight x space straight y end exponent space equals space straight y rightwards double arrow straight a equals open parentheses 1 third close parentheses to the power of 4 equals 1 over 81 left parenthesis iii right parenthesis log subscript straight a space 1 equals 0 rightwards double arrow straight a to the power of log subscript straight a space 1 end exponent equals straight a to the power of 0 rightwards double arrow straight a equals 1 left parenthesis iv right parenthesis log subscript 3 space left parenthesis straight a squared plus 1 right parenthesis equals 1 rightwards double arrow 3 to the power of log subscript 3 space left parenthesis straight a squared plus 1 right parenthesis end exponent equals 3 to the power of 1 rightwards double arrow straight a squared plus 1 equals 3 rightwards double arrow straight a squared equals 2 rightwards double arrow straight a equals plus-or-minus square root of 2

Answered by Renu Varma | 19 Dec, 2022, 11:15: AM

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