WEBVTT 00:00:01.650 --> 00:00:09.110 Calculate two log four plus seven log 13, giving you answer to the nearest thousandth. 00:00:10.340 --> 00:00:13.860 We could type our expression directly into the calculator. 00:00:14.300 --> 00:00:20.520 However, in this case, we will simplify the expression first using our laws of logarithms. 00:00:22.040 --> 00:00:29.140 One of the laws of logarithms states that 𝑛 log π‘Ž is equal to log π‘Ž to the power of 𝑛. 00:00:30.300 --> 00:00:35.490 The number that we are multiplying the logarithm by becomes the exponent or power. 00:00:36.830 --> 00:00:43.270 This means that our first term, two log four, can be rewritten as log of four squared. 00:00:44.530 --> 00:00:50.770 In the same way, seven log 13 is the same as log 13 to the power of seven. 00:00:52.410 --> 00:00:59.480 Another one of our laws of logarithms states that log π‘Ž plus log 𝑏 is equal to log of π‘Žπ‘. 00:01:00.900 --> 00:01:09.350 Our expression can therefore be simplified to log of four squared multiplied by 13 to the power of seven. 00:01:10.590 --> 00:01:21.970 Whilst we could calculate four squared multiplied by 13 to the power of seven, as 13 to the power of seven is so large, we will leave it in this form in this question. 00:01:23.240 --> 00:01:30.790 Typing this into the calculator gives us 9.001723 and so on. 00:01:31.630 --> 00:01:34.170 We’re asked to round to the nearest thousandth. 00:01:34.410 --> 00:01:37.700 This is the same as rounding to three decimal places. 00:01:39.030 --> 00:01:41.230 The seven becomes the deciding number. 00:01:41.540 --> 00:01:45.400 And if the deciding number is five or greater, we round up. 00:01:46.820 --> 00:01:54.750 Two log four plus seven log 13 to the nearest thousandth is 9.002. 00:01:56.490 --> 00:02:01.310 Note that in this question, there was no base number in either of our terms. 00:02:01.680 --> 00:02:09.130 If this is the case, we assume that it is log of base 10 and use the log button on our calculator. 00:02:11.010 --> 00:02:19.570 10 to the power of 9.002 would be equal to two log four plus seven log 13.