Math HL 12th IBSTEP by STEP INTERNATIONAL SCHOOL WorksheetEXP
& LOGARITHMS1. Let be the angle between the unit vectors a and
b, where 0 .(a) Express a b and a + b in terms of .(b) Hence
determine the value of cos for which a + b!a b.2. "olve the
following s#stem of e$uations.logx+% y&logy+% x413. "olve the
e$uation log!(x + %') &log! &x. 4. "olve the e$uation
&&x+& %0 ( &x + )0* x . 5. "olve the e$uation
)x%&x + +.Math HL 12th IBSTEP by STEP INTERNATIONAL SCHOOL
WorksheetEXP & LOGARITHMS1. Let be the angle between the unit
vectors a and b, where 0 .(a) Express a b and a + b in terms of
.(b) Hence determine the value of cos for which a + b!a b.2. "olve
the following s#stem of e$uations.logx+% y&logy+% x413. "olve
the e$uation log!(x + %') &log! &x. 4. "olve the e$uation
&&x+& %0 ( &x + )0* x . 5. "olve the e$uation
)x%&x + +.6. "olve the e$uations1 ln =yxln x! + ln y&,. 7.
(a) -ind the solution of the e$uationln &)x%ln +x+, +
log&%.%&x*expressing #our answer in terms of ln &.(b)
/sing this value of x* 0nd the value of a for which logax&*
giving #our answer to three decimal places. . 1rite ln (x& %)
& ln(x + %) + ln(x& + x) as a single logarithm* in its
simplest form. !. Let g(x)log,&log!x. -ind the product of the
2eros of g.6. "olve the e$uations1 ln =yxln x! + ln y&,. 7. (a)
-ind the solution of the e$uationln &)x%ln +x+, +
log&%.%&x*expressing #our answer in terms of ln &.(b)
/sing this value of x* 0nd the value of a for which logax&*
giving #our answer to three decimal places. . 1rite ln (x& %)
& ln(x + %) + ln(x& + x) as a single logarithm* in its
simplest form. !. Let g(x)log,&log!x. -ind the product of the
2eros of g.
