Question

If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:

(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0

Answer 1

Answer:

Step-by-step explanation:

(0.2)x = 2.

Taking log on both sides

log (0.2)x = log 2.

x log (0.2) = 0.3010, [since log 2 = 0.3010].

x log (2/10) = 0.3010.

x [log 2 - log 10] = 0.3010.

x [log 2 - 1] = 0.3010,[since log 10=1].

x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].

x[-0.699] = 0.3010.

x = 0.3010/-0.699.

x = -0.4306….

x = -0.4 (nearest tenth)

Answer: (c)

Answer 2

Given :-- (0.2)x = 2 , log2 = 0.3010

Question :--- Find value of x ?

Solution :-----

0.2x = 2

Taking log both sides we get,

$xlog( \frac{2}{10} ) = log2 \\ \\ now \: we \: know \: that \: \\ \\ log( \frac{x}{y} ) = logx - logy$

Using this we get,

x(log2-log10) = 0.3010

now, we know that

log10 = 1

so,

x(log2-1) = 0.3010

x(0.3010-1) = 0.3010

x(-0.699) = 0.3010

x = $\huge{\frac{</strong><strong>0</strong><strong>.</strong><strong>3</strong><strong>0</strong><strong>1</strong><strong>0</strong><strong>}{</strong><strong>(</strong><strong>-</strong><strong>0</strong><strong>.</strong><strong>6</strong><strong>9</strong><strong>9</strong><strong>)</strong><strong>}}$

$\large\red{\boxed{\sf </strong><strong>x</strong><strong>=</strong><strong>(</strong><strong>-</strong><strong>0</strong><strong>.</strong><strong>4</strong><strong>)</strong><strong>}}$

(C) Answer