log3 + logx=4
log(3x)=4
3x=10^4
x=10,000/3
Use the identity log(ab) = log a + log b to combine the logarithms on the left side into a single term. Then take antilogarithms (just take the log away) on both sides.
You can't solve this since it isn't an equation.There is also an ambiguity (it's hard to write math on a typewriter keyboard) - are we talking about log(x3) or maybe logx(3)?Restate the question: Simplify log(x3)Answer: 3log(x)You could explain this by saying: log(x3) = log[(x)(x)(x)] = logx + logx + logx = 3logx. The general rule is log(xn) = nlogx.
logx(3) = log10(7) (assumed the common logarithm (base 10) for "log7") x^(logx(3)) = x^(log10(7)) 3 = x^(log10(7)) log10(3) = log10(x^(log10(7))) log10(3) = log10(7)log10(x) (log10(3)/log10(7)) = log10(x) 10^(log10(3)/log10(7)) = x
We can't see the parentheses, and there are at least two ways to read this.Here are solutions for the most likely two:--------------------------------------------------------log(x) - 3 + log(x) - 2 = log(2x) + 24Add 5 to each side:log(x) + log(x) = log(2x) + 29Subtract log(2x) from each side:log(x) + log(x) - log(2x) = 29Combine the logs on the left side, and massage:log( x2/2x ) = log( x/2 ) = 29Take the antilog of each side:x/2 = 1029Multiply each side by 2:x = 2 x 1029------------------------------------------------log(x - 3) + log(x - 2) = log(2x + 24)Combine logs on the left side:log[ (x-3) (x-2) ] = log(2x + 24)Take antilog of each side:(x-3) (x-2) = 2x + 24Expand the left side:x2 - 5x +6 = 2x + 24Subtract (2x+24) from each side:x2 - 7x - 18 = 0Factor:(x - 9) (x + 2) = 0Whence:x = 9x = -2We have to discard the solution [ x = -2 ] because one term in the equationis log(x-2).If 'x' were -2 then we'd have log(-4) but negative numbers don't have logs.
-Log(1.4x10-3)= 2.85 The Log to be used here is the decimal one, not the neperian one.
logx^3logx^2log14 is 3logx2logxlog14 this equals 6 log14 (logx)^2 So for example, if y=6log14(logx)^2 the log x = square root of (y/6(log14))
Use the identity log(ab) = log a + log b to combine the logarithms on the left side into a single term. Then take antilogarithms (just take the log away) on both sides.
x^3=27 then switch it logx^27=3
You can't solve this since it isn't an equation.There is also an ambiguity (it's hard to write math on a typewriter keyboard) - are we talking about log(x3) or maybe logx(3)?Restate the question: Simplify log(x3)Answer: 3log(x)You could explain this by saying: log(x3) = log[(x)(x)(x)] = logx + logx + logx = 3logx. The general rule is log(xn) = nlogx.
Without brackets, there are many ambiguities in the question. 4 = 2/3*log(x) - 0.9 4.9*3/2 = logx 7.35 = logx so x = 107.35 However, the original equation could also have referred to 4 = 2/3*log(x-0.9) or 4 = 2/[3*log(x)] - 0.9 or 4 = 2/[3*log(x-0.9)]
*First off if we assume this log to be base 10 next we can use the product rule (d/dx (3)*logx+d/dx(logx)*3) 1.derivative of a constant is zero so that gives us 0*logx as our first term (simplifies to zero) next we have to differentiate logx that gives us 3*(1/xln(10)) so that leaves 0logx+3*(1/xln(10)) simplify...... 3/xln(10)
logx(3) = log10(7) (assumed the common logarithm (base 10) for "log7") x^(logx(3)) = x^(log10(7)) 3 = x^(log10(7)) log10(3) = log10(x^(log10(7))) log10(3) = log10(7)log10(x) (log10(3)/log10(7)) = log10(x) 10^(log10(3)/log10(7)) = x
3^(-2x + 2) = 81? log(3^(-2x + 2)) = log(81) (-2x+2)log(3) = log(81) -2x = log(81)/log(3) - 2 x = (-1/2)(log(81)/log(3)) + 1
We can't see the parentheses, and there are at least two ways to read this.Here are solutions for the most likely two:--------------------------------------------------------log(x) - 3 + log(x) - 2 = log(2x) + 24Add 5 to each side:log(x) + log(x) = log(2x) + 29Subtract log(2x) from each side:log(x) + log(x) - log(2x) = 29Combine the logs on the left side, and massage:log( x2/2x ) = log( x/2 ) = 29Take the antilog of each side:x/2 = 1029Multiply each side by 2:x = 2 x 1029------------------------------------------------log(x - 3) + log(x - 2) = log(2x + 24)Combine logs on the left side:log[ (x-3) (x-2) ] = log(2x + 24)Take antilog of each side:(x-3) (x-2) = 2x + 24Expand the left side:x2 - 5x +6 = 2x + 24Subtract (2x+24) from each side:x2 - 7x - 18 = 0Factor:(x - 9) (x + 2) = 0Whence:x = 9x = -2We have to discard the solution [ x = -2 ] because one term in the equationis log(x-2).If 'x' were -2 then we'd have log(-4) but negative numbers don't have logs.
-Log(1.4x10-3)= 2.85 The Log to be used here is the decimal one, not the neperian one.
If the log of x equals -3 then x = 10-3 or 0.001or 1/1000.
2 log(x) + 3 log(x) = 105 log(x) = 10log(x) = 10/5 = 210log(x) = (10)2x = 100