Please note that an expression like log 25.65 is ambiguous, since no base is specified. In this case, either base 10 or base e might be assumed, depending on the context.
In some calculators, especially older ones, you would press the number 25.65, then press one of the log keys. There is usually one for base 10, and one for base e. In newer calculators, you press the one of the log keys first, then the number, then something like enter.
0.3679
Let y = log3 x⇒ x = 3yTaking logs to any base you like of both sides gives:log x = y log 3⇒ y = log x/log 3So to calculate log base 3 on a calculator, use either the [log] (common or log to base 10) or [ln] (natural or to base e) function key for the log above, that is use one of:[(] [log] [] [÷] [log] [3] [)][(] [ln] [] [÷] [ln] [3] [)][(] [] [log] [÷] [3] [log] [)][(] [] [ln] [÷] [3] [ln] [)]Things in square brackets [] represent keys on the calculator; the is the number of which you want the logarithm to base 3.Use one of 1 & 1 if your calculator is a more modern one that uses natural representation that looks like maths whereby the calculation is done once you've finished entering it all and the numbers for functions follow them.Use one of 3 & 4 if your calculator is an older style one that when you press a function key it acts immediately on the number displayed on the screen.The parentheses (round brackets) are included above so that the whole expression evaluates to log3.
If we take the logarithm of both sides, then it is log(4^x) = log(128). Then from logarithm rules, this can be changed to: x*log(4) = log(128), then x = log(128)/log(4). You can punch this into a calculator and get the answer, but what if we use log base 2, we don't need a calculator. So log2(4) = 2, because 2² = 4. And log2(128) = 7, because 2^7 = 128. So we have x = 7/2 = 3.5, then you can check your answer: 4^3.5 = (4^3)*(4^.5). So 4 cubed = 64, and 4 raised to the 1/2 power is the square root of 4, which is 2. So 64 times 2 = 128.
2x = 0.5: This is like asking for the logarithm of 0.5, to the base 2. A scientific calculator normally has logarithms for base 10 and base e, but not for other bases. However, you can calculate this is log(0.5) / log(2). It doesn't matter what base you use for your logarithms, just keep it consistent. For example, with base 10, log(0.5) / log(2) = -0.301 / 0.301 = -1.
log0.1 50 = log10 50 / log10 0.1 ~= -1.699 To work out the log to any base b, logs to another base can be used: When logs are taken of a number to a power, then the power is multiplied by the log of the number, that is: log(bn) = n log b Taking logs to base b the power of b that equals the original number is being found, that is if: bn = m then logb m = n So, by using the logs to a base to which the answer can be known, the log to any base can be calculated: bn = m => n log b = log m => n = log m / log b => logb m = log m / log b as long as the same base is used for the logs on the right. It is normal to use base 10 or base e which are found on calculator buttons marked log (base 10) and ln (log natural - base e).
You can calculate that on any scientific calculator - like the calculator on Windows (if you change the options, to display as a scientific calculator). Log base 4 of 27 is the same as log 27 / log 4. You can use logarithms in any base to calculate that - just use the same base for both logarithms.
You should use a calculator for a question like this. It is quicker and simpler. Log(14) = 1.15
If you are using a scientific calculator you will have a key labelled "log". To find the logarithm (to base 10) of a number, simply enter "log" followed by the number that you want to log. If you want a natural logarithm - log to the base e - use the "ln" key instead. If you haven't got a scientific calculator, use the one on your computer.
124.3784
You look them up in log tables, or use a scientific calculator. The calculators use a method based on the Taylor series.
To find anti log of a number enter the number as the exponent of 10.
The anti-log is "10^x" listed above the "LOG" key on a TI-86 calculator. All you have to do to use it is press the yellow "2nd" key (this means shift) and then press the "LOG" key.
0.3679
Look it up in table of logarithms or use "log" button on scientific or other calculator. You might even be able to Google it!
The inverse of a logarithmic function is an exponential function. So to find the "inverse" of the log function, you use the universal power key, unless you're finding the inverse of a natural log, then you use the e^x key.
You can do it directly on a calculator and get 1.2676506002282e+30. Or you can use logs like y=n^5 and log y=5*log(1048576)=30.102999566398. Look up the anti-log for the answer.
Let y = log3 x⇒ x = 3yTaking logs to any base you like of both sides gives:log x = y log 3⇒ y = log x/log 3So to calculate log base 3 on a calculator, use either the [log] (common or log to base 10) or [ln] (natural or to base e) function key for the log above, that is use one of:[(] [log] [] [÷] [log] [3] [)][(] [ln] [] [÷] [ln] [3] [)][(] [] [log] [÷] [3] [log] [)][(] [] [ln] [÷] [3] [ln] [)]Things in square brackets [] represent keys on the calculator; the is the number of which you want the logarithm to base 3.Use one of 1 & 1 if your calculator is a more modern one that uses natural representation that looks like maths whereby the calculation is done once you've finished entering it all and the numbers for functions follow them.Use one of 3 & 4 if your calculator is an older style one that when you press a function key it acts immediately on the number displayed on the screen.The parentheses (round brackets) are included above so that the whole expression evaluates to log3.