Q&A for How to Solve Logarithms

Logarithmic graphs have asymptotes at x=0, therefore any negative answers cannot exist.

Understand that the antilog of 12.18 is a common antilogarithm question, which means the assumed subscript is 10. To solve this problem, take 10 to the power of 12.18. This gives you an approximate value of 1,513,561,248,436.21.

4^x + 10 = 10. Subtract 10 from both sides. 4^x = 0. Rewrite according to the definition of a logarithm. log4(0) = x. Use the change of base formula to calculate log4(0). log(0)/log(4) = x log(0) is undefined, making x undefined as well.

Since this equation hasn't been set equal to anything and has no x's to solve for, we can solve by simply plugging it into a calculator, giving us 5.799025... as our answer.

First, simplify the left-hand side. As a rule, log(a) - log(b) = log(a/b), so we rewrite as: log10[(x+2) / (x-1)] = 2. Next we need to convert the right-hand side to a logarithm so we can cancel them out on both sides. Because loga(a) = 1 (log of a to base a), log10[(x+2) / (x-1)] = 2*log10(10). The right-hand side MUST then be written as log10(10^2) BEFORE attempting to cancel out the logs, since nlog(a) = log(a^n). Cancelling out the logarithms from both sides leaves us with: (x+2) / (x-1) = 100. From here, we simply solve for x using basic algebra: x+2 = 100(x-1) x+2 = 100x - 100 100x - x = 2 + 100 99x = 102 x = 102/99.

Try to find 168.75 in terms of 16 and 81. After trying to divide by 16 and 81, you can determine that 25x81/12 = 168.75. Since we have the term 81 as a factor, we have to try to find 16 as a factor. We can find the factors of 16 as 4x4, 2x2x2x2 and the factors of 12 as 3x4. We can neglect 25, because it is 5x5 and there are no common factors with 81 and 16. Multiply top and bottom by 4 to get 4x25x81/(3x4x4) = 100x81/(3x16). Now that we have our factors, we can express it in terms of m and n by taking logarithms. Log(100x81/(3x16)) = log(100) + log(81) - (log(3) + log(16)). Using properties of log, log(81)=log(9²)=2log(9)=2log(3²)=4log(3)=n, so log(3)=n/4. Log(100) is log(10²) or 2log(10)=2x1. By substitution, log(100x81/(3x16))=2+n-n/4-m=2+3n/4+m.

3log10 (3)=log10 (1/x) => log10 (3^3)=log10 (1/x) or 3^3=1/x, which gives x=1/(3^3) or 1/27

Find log2(32). You get 5. So log2(x + 2) - 2 = 5 and log2(x + 2) = 7. Then put 2 as the base for both sides: x + 2 = 2⁷ = 128, so that x = 128 - 2 = 126.