Question

Write the following relation in expontial form and find the values of respective variables
log2 32=x
Log5 625=y
Log10 10000=z
Log7 1/343=-a

Answer 1

2^x=32; x = 5
5^y=625; y = 4
10^z=10000; z=4
7^-a=1/343; 7^a=343; a=3

PS all the answers were found by looping thru different values for the variables with a calculator

Answer 2

Answer:

The value of variables x, y, z and a is 5, 4, 4, and 3 respectively.

Step-by-step explanation:

A logarithmic expression is given by :

$log_{y}x=n$

The same expression can be shown in the exponential form as follows:

$log_{y}x=n\\x=y^{n}$

Thus, for the four given logarithmic expressions, we can write them in the exponential form and calculate the value of the variables as follows:

$i)\\log_{2}32=x\\32=2^{x} \\2^5=2^x\\x=5\\\\ii)\\log_{5}625=y\\625=5^{y} \\5^4=5^y\\y=4\\\\iii)\\log_{10}10000=z\\10000=10^{z} \\10^4=10^z\\z=4\\\\iv)\\log_{7}(\frac{1}{343}) =-a\\\\\frac{1}{343}=7^{-a} \\\\7^3=7^a\\a=3$

Thus, the value of variables x, y, z, and a is 5, 4, 4, and 3 respectively.

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