標題:
F4 maths(20marks)
發問:
1.) If log2.5=k,expressof the following in terms of k. log 0.42) if f(x)=2^x-k*2^-x and 2f(1)=3,find the value of k and the value of x such that f(x)=63/83) solve the equation2^(2x+3)-4^x=35 (give the answer correct to... 顯示更多 1.) If log2.5=k,expressof the following in terms of k. log 0.4 2) if f(x)=2^x-k*2^-x and 2f(1)=3,find the value of k and the value of x such that f(x)=63/8 3) solve the equation2^(2x+3)-4^x=35 (give the answer correct to 3significant figures.) 4) simplify (log x^3-log y)/(log (1/x)+logy^1/3 5) solve the simultaneous equations: log y=log(x+2)-1 2x-5y=26
最佳解答:
Ans and steps as follows: 1) log 0.4 = log 2/5 = log 2 - log 5 = - ( log 5 - log 2 ) = - log 5/2 = - log 2.5 = -k ==== 2) f(x) = 2^x - k( 2^-x ) f(1) = 2 - k/2 = 3/2k = 1Hence, f(x) = 2^x - 2^-x Set f(x) = 63/88( 2^2x ) - 63( 2^x ) - 8 = 0 [ 8( 2^x ) + 1 ][ ( 2^x ) - 8 ] = 0 2^x = -1/8 ( rejected ) or 2^x = 8 = 2^3 x = 3 ===== 3) 2^( 2x + 3 ) - 4^x = 35 2^( 2x + 3 ) - 2^2x = 352^2x ( 2^3 - 1 ) = 352^2x = 35/7 = 52x log 2 = log 5x = log 5 / 2 log 2 ============== [ Please use your Cal. to check the ans. ] 4) ( log x^3 - log y ) / [ log (1/x ) + log y^1/3 ] = ( 3log x - log y )( -log x + 1/3 log y ) = ( 3log x - log y )/[ -1/3 ( 3log x - log y ) = -3( 3log x - log y )/( 3log x - log y ) = -3 === 5) log y = log ( x + 2 ) - 1 log y = log ( x + 2 ) - log 10 log y = log [ ( x + 2 ) / 10 ] y = ( x + 2 ) / 10 10y = x + 2 x - 10y = -2 ------- (1) 2x - 5y = 26 ----- (2) Solve by Elimination Method, ( x, y ) = ( 18, 2 ) ============ Hope I can help you.
F4 maths(20marks)
發問:
1.) If log2.5=k,expressof the following in terms of k. log 0.42) if f(x)=2^x-k*2^-x and 2f(1)=3,find the value of k and the value of x such that f(x)=63/83) solve the equation2^(2x+3)-4^x=35 (give the answer correct to... 顯示更多 1.) If log2.5=k,expressof the following in terms of k. log 0.4 2) if f(x)=2^x-k*2^-x and 2f(1)=3,find the value of k and the value of x such that f(x)=63/8 3) solve the equation2^(2x+3)-4^x=35 (give the answer correct to 3significant figures.) 4) simplify (log x^3-log y)/(log (1/x)+logy^1/3 5) solve the simultaneous equations: log y=log(x+2)-1 2x-5y=26
最佳解答:
Ans and steps as follows: 1) log 0.4 = log 2/5 = log 2 - log 5 = - ( log 5 - log 2 ) = - log 5/2 = - log 2.5 = -k ==== 2) f(x) = 2^x - k( 2^-x ) f(1) = 2 - k/2 = 3/2k = 1Hence, f(x) = 2^x - 2^-x Set f(x) = 63/88( 2^2x ) - 63( 2^x ) - 8 = 0 [ 8( 2^x ) + 1 ][ ( 2^x ) - 8 ] = 0 2^x = -1/8 ( rejected ) or 2^x = 8 = 2^3 x = 3 ===== 3) 2^( 2x + 3 ) - 4^x = 35 2^( 2x + 3 ) - 2^2x = 352^2x ( 2^3 - 1 ) = 352^2x = 35/7 = 52x log 2 = log 5x = log 5 / 2 log 2 ============== [ Please use your Cal. to check the ans. ] 4) ( log x^3 - log y ) / [ log (1/x ) + log y^1/3 ] = ( 3log x - log y )( -log x + 1/3 log y ) = ( 3log x - log y )/[ -1/3 ( 3log x - log y ) = -3( 3log x - log y )/( 3log x - log y ) = -3 === 5) log y = log ( x + 2 ) - 1 log y = log ( x + 2 ) - log 10 log y = log [ ( x + 2 ) / 10 ] y = ( x + 2 ) / 10 10y = x + 2 x - 10y = -2 ------- (1) 2x - 5y = 26 ----- (2) Solve by Elimination Method, ( x, y ) = ( 18, 2 ) ============ Hope I can help you.
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