Friday

March 6, 2015

March 6, 2015

Posted by **Jenny** on Monday, December 6, 2010 at 10:33pm.

Solve for x in terms of a and b:

6^x = 10/3 - 6^-x

- calculus-watch parentheses -
**MathMate**, Monday, December 6, 2010 at 11:32pmParentheses are not needed for fractions in type-set texts because it is graphically clear. When transferred to a one-line expression, parentheses are required around the numerator and denominator.

I assume the question is as follows, which is different from what you posted because of the missing parentheses.

6^x=10/(3-6^(-x)) ....(1)

From log(2)=a, and log(3)=b,

we deduce that

e^{a}=2, and

e^{b}=3.

cross multiply (1), assume 3≠6^(-x)

6^x(3-6^(-x))=10

3*6^x - 6^0 = 10 .... (6^0 = 1)

3*6^x = 11

6^x = 11/3

take log on both sides

x(log(2)+log(3) = log(11)-log(3)

x = (log(11)-b)/(a+b)

**Answer this Question**

**Related Questions**

maths pls help - 1. Solve the following simultaneous equations: log2 xy = 7 log2...

maths - 1.Log10(x²-12x+36)=2 2.log4 log3 log2 x=0 3.log3 [log9x+1/2+9x]=2x 4....

calculus - 1) Solve for x in terms of k: log3(x) + log3(x+7) = k; 3 is the base ...

Math - logs - log_3(2x - 1) = 2, Find x. Here's what I've done: log_3(2x) * ...

trig - solve for x log4 64+ log2 2 ________________ =x log3 81

Logarithmic Algebra - let log2=a, log3=b, and log5=c. express the indicated ...

Math Algebra 2 - How do I put log in a TI-84 calculator. #1.Express the ...

math - solve the equation log2(x+4)-log4x=2 the 2 and 4 are lower than the g ...

Precalculus - Please help me with these questions ASAP!! Suppose that f(x)=log3...

add maths - Given that log2 3=h and log2 5=k, express log2 0.45 in terms of h ...